Mixing
I need help solving a competition math problem.
$begingroup$
I was doing a practice test for a math competition, and I came across a problem I am unable to solve, and I have tried to get help, with no luck. I need to be able to solve it without a calculator too. The problem is: "If $x^2+1/x^2=3$ and $x > 0$, what is the value of $x+1/x$. Express your answer in simplest radical form." I tried manipulating the first equation and I end up with $x^4-3x^2+1=0$, and there is no way I can figure out how to factor it. I would appreciate any help I can get with this problem!
polynomials contest-math
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
$endgroup$
add a comment |
$begingroup$
I was doing a practice test for a math competition, and I came across a problem I am unable to solve, and I have tried to get help, with no luck. I need to be able to solve it without a calculator too. The problem is: "If $x^2+1/x^2=3$ and $x > 0$, what is the value of $x+1/x$. Express your answer in simplest radical form." I tried manipulating the first equation and I end up with $x^4-3x^2+1=0$, and there is no way I can figure out how to factor it. I would appreciate any help I can get with this problem!
polynomials contest-math
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
$endgroup$
add a comment |
$begingroup$
I was doing a practice test for a math competition, and I came across a problem I am unable to solve, and I have tried to get help, with no luck. I need to be able to solve it without a calculator too. The problem is: "If $x^2+1/x^2=3$ and $x > 0$, what is the value of $x+1/x$. Express your answer in simplest radical form." I tried manipulating the first equation and I end up with $x^4-3x^2+1=0$, and there is no way I can figure out how to factor it. I would appreciate any help I can get with this problem!
polynomials contest-math
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
$endgroup$
I was doing a practice test for a math competition, and I came across a problem I am unable to solve, and I have tried to get help, with no luck. I need to be able to solve it without a calculator too. The problem is: "If $x^2+1/x^2=3$ and $x > 0$, what is the value of $x+1/x$. Express your answer in simplest radical form." I tried manipulating the first equation and I end up with $x^4-3x^2+1=0$, and there is no way I can figure out how to factor it. I would appreciate any help I can get with this problem!
polynomials contest-math
polynomials contest-math
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
asked Jan 30 at 2:45
Spencer1O1Spencer1O1
125
125
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Guide:
Let $y=x^2$, solve for $y$ using the quadratic formula.
After you get your $y$, you can solve for the corresponding $x$.
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
$begingroup$
Can I get a more detailed explanation? I know the quadratic formula, but that doesn't really answer my question.
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
can you solve $y^2-3y+1=0$?
$endgroup$
– Siong Thye Goh
Jan 31 at 0:53
add a comment |
$begingroup$
Notice that $x^2 frac{1}{x^2} = 1$. We could add 2 to both sides of the equation to complete the square. $$ (x + frac{1}{x})^2 = 5$$
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
$begingroup$
You mean $x^2 + frac 1 {x^2}=3?$
$endgroup$
– J. W. Tanner
Jan 30 at 2:59
$begingroup$
Thank you for pointing out the typo, I mean their product. It is corrected. @J.W.Tanner
$endgroup$
– Alvis Nordkovich
Jan 30 at 3:04
$begingroup$
Can I get a more detailed explanation please?
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
$$x^2 + frac{1}{x^2} + 2 = 3 + 2 = 5$$ $$x^2 + x^2 frac{1}{x^2} + frac{1}{x^2} = 5$$ $$(x+frac{1}{x})^2 = 5$$ $$x + frac{1}{x} = sqrt{5}$$ given $x > 0$ @Spencer1O1
$endgroup$
– Alvis Nordkovich
Jan 31 at 1:31
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Guide:
Let $y=x^2$, solve for $y$ using the quadratic formula.
After you get your $y$, you can solve for the corresponding $x$.
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
$begingroup$
Can I get a more detailed explanation? I know the quadratic formula, but that doesn't really answer my question.
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
can you solve $y^2-3y+1=0$?
$endgroup$
– Siong Thye Goh
Jan 31 at 0:53
add a comment |
$begingroup$
Guide:
Let $y=x^2$, solve for $y$ using the quadratic formula.
After you get your $y$, you can solve for the corresponding $x$.
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
$begingroup$
Can I get a more detailed explanation? I know the quadratic formula, but that doesn't really answer my question.
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
can you solve $y^2-3y+1=0$?
$endgroup$
– Siong Thye Goh
Jan 31 at 0:53
add a comment |
$begingroup$
Guide:
Let $y=x^2$, solve for $y$ using the quadratic formula.
After you get your $y$, you can solve for the corresponding $x$.
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
$endgroup$
Guide:
Let $y=x^2$, solve for $y$ using the quadratic formula.
After you get your $y$, you can solve for the corresponding $x$.
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
answered Jan 30 at 2:48
Siong Thye GohSiong Thye Goh
103k1468120
103k1468120
$begingroup$
Can I get a more detailed explanation? I know the quadratic formula, but that doesn't really answer my question.
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
can you solve $y^2-3y+1=0$?
$endgroup$
– Siong Thye Goh
Jan 31 at 0:53
add a comment |
$begingroup$
Can I get a more detailed explanation? I know the quadratic formula, but that doesn't really answer my question.
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
can you solve $y^2-3y+1=0$?
$endgroup$
– Siong Thye Goh
Jan 31 at 0:53
$begingroup$
Can I get a more detailed explanation? I know the quadratic formula, but that doesn't really answer my question.
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
Can I get a more detailed explanation? I know the quadratic formula, but that doesn't really answer my question.
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
can you solve $y^2-3y+1=0$?
$endgroup$
– Siong Thye Goh
Jan 31 at 0:53
$begingroup$
can you solve $y^2-3y+1=0$?
$endgroup$
– Siong Thye Goh
Jan 31 at 0:53
add a comment |
$begingroup$
Notice that $x^2 frac{1}{x^2} = 1$. We could add 2 to both sides of the equation to complete the square. $$ (x + frac{1}{x})^2 = 5$$
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
$begingroup$
You mean $x^2 + frac 1 {x^2}=3?$
$endgroup$
– J. W. Tanner
Jan 30 at 2:59
$begingroup$
Thank you for pointing out the typo, I mean their product. It is corrected. @J.W.Tanner
$endgroup$
– Alvis Nordkovich
Jan 30 at 3:04
$begingroup$
Can I get a more detailed explanation please?
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
$$x^2 + frac{1}{x^2} + 2 = 3 + 2 = 5$$ $$x^2 + x^2 frac{1}{x^2} + frac{1}{x^2} = 5$$ $$(x+frac{1}{x})^2 = 5$$ $$x + frac{1}{x} = sqrt{5}$$ given $x > 0$ @Spencer1O1
$endgroup$
– Alvis Nordkovich
Jan 31 at 1:31
add a comment |
$begingroup$
Notice that $x^2 frac{1}{x^2} = 1$. We could add 2 to both sides of the equation to complete the square. $$ (x + frac{1}{x})^2 = 5$$
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
$begingroup$
You mean $x^2 + frac 1 {x^2}=3?$
$endgroup$
– J. W. Tanner
Jan 30 at 2:59
$begingroup$
Thank you for pointing out the typo, I mean their product. It is corrected. @J.W.Tanner
$endgroup$
– Alvis Nordkovich
Jan 30 at 3:04
$begingroup$
Can I get a more detailed explanation please?
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
$$x^2 + frac{1}{x^2} + 2 = 3 + 2 = 5$$ $$x^2 + x^2 frac{1}{x^2} + frac{1}{x^2} = 5$$ $$(x+frac{1}{x})^2 = 5$$ $$x + frac{1}{x} = sqrt{5}$$ given $x > 0$ @Spencer1O1
$endgroup$
– Alvis Nordkovich
Jan 31 at 1:31
add a comment |
$begingroup$
Notice that $x^2 frac{1}{x^2} = 1$. We could add 2 to both sides of the equation to complete the square. $$ (x + frac{1}{x})^2 = 5$$
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
$endgroup$
Notice that $x^2 frac{1}{x^2} = 1$. We could add 2 to both sides of the equation to complete the square. $$ (x + frac{1}{x})^2 = 5$$
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
edited Jan 30 at 3:03
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
answered Jan 30 at 2:50
Alvis NordkovichAlvis Nordkovich
256110
256110
$begingroup$
You mean $x^2 + frac 1 {x^2}=3?$
$endgroup$
– J. W. Tanner
Jan 30 at 2:59
$begingroup$
Thank you for pointing out the typo, I mean their product. It is corrected. @J.W.Tanner
$endgroup$
– Alvis Nordkovich
Jan 30 at 3:04
$begingroup$
Can I get a more detailed explanation please?
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
$$x^2 + frac{1}{x^2} + 2 = 3 + 2 = 5$$ $$x^2 + x^2 frac{1}{x^2} + frac{1}{x^2} = 5$$ $$(x+frac{1}{x})^2 = 5$$ $$x + frac{1}{x} = sqrt{5}$$ given $x > 0$ @Spencer1O1
$endgroup$
– Alvis Nordkovich
Jan 31 at 1:31
add a comment |
$begingroup$
You mean $x^2 + frac 1 {x^2}=3?$
$endgroup$
– J. W. Tanner
Jan 30 at 2:59
$begingroup$
Thank you for pointing out the typo, I mean their product. It is corrected. @J.W.Tanner
$endgroup$
– Alvis Nordkovich
Jan 30 at 3:04
$begingroup$
Can I get a more detailed explanation please?
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
$$x^2 + frac{1}{x^2} + 2 = 3 + 2 = 5$$ $$x^2 + x^2 frac{1}{x^2} + frac{1}{x^2} = 5$$ $$(x+frac{1}{x})^2 = 5$$ $$x + frac{1}{x} = sqrt{5}$$ given $x > 0$ @Spencer1O1
$endgroup$
– Alvis Nordkovich
Jan 31 at 1:31
$begingroup$
You mean $x^2 + frac 1 {x^2}=3?$
$endgroup$
– J. W. Tanner
Jan 30 at 2:59
$begingroup$
You mean $x^2 + frac 1 {x^2}=3?$
$endgroup$
– J. W. Tanner
Jan 30 at 2:59
$begingroup$
Thank you for pointing out the typo, I mean their product. It is corrected. @J.W.Tanner
$endgroup$
– Alvis Nordkovich
Jan 30 at 3:04
$begingroup$
Thank you for pointing out the typo, I mean their product. It is corrected. @J.W.Tanner
$endgroup$
– Alvis Nordkovich
Jan 30 at 3:04
$begingroup$
Can I get a more detailed explanation please?
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
Can I get a more detailed explanation please?
$endgroup$
– Spencer1O1
Jan 30 at 23:02
$begingroup$
$$x^2 + frac{1}{x^2} + 2 = 3 + 2 = 5$$ $$x^2 + x^2 frac{1}{x^2} + frac{1}{x^2} = 5$$ $$(x+frac{1}{x})^2 = 5$$ $$x + frac{1}{x} = sqrt{5}$$ given $x > 0$ @Spencer1O1
$endgroup$
– Alvis Nordkovich
Jan 31 at 1:31
$begingroup$
$$x^2 + frac{1}{x^2} + 2 = 3 + 2 = 5$$ $$x^2 + x^2 frac{1}{x^2} + frac{1}{x^2} = 5$$ $$(x+frac{1}{x})^2 = 5$$ $$x + frac{1}{x} = sqrt{5}$$ given $x > 0$ @Spencer1O1
$endgroup$
– Alvis Nordkovich
Jan 31 at 1:31
add a comment |
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