Mixing
Phenomena relating to the condition ($ab = cd$ or $a + b ne c + d$)
Given numbers $a, b, c,; text{and}; d$ (not necessarily distinct), what phenomena is the condition $(ab = cd ; text{or} ; a + b neq c + d)$ linked to? I came across one, but I wanted to see if there were any others before revealing it.
algebra-precalculus
edited Nov 20 '18 at 23:11
user376343
2,8582823
asked Nov 20 '18 at 15:10
EulerSpoiler
729
add a comment |
Given numbers $a, b, c,; text{and}; d$ (not necessarily distinct), what phenomena is the condition $(ab = cd ; text{or} ; a + b neq c + d)$ linked to? I came across one, but I wanted to see if there were any others before revealing it.
algebra-precalculus
edited Nov 20 '18 at 23:11
user376343
2,8582823
asked Nov 20 '18 at 15:10
EulerSpoiler
729
2
Please explain "I came accross one". Provide the proof here please.
– Sujit Bhattacharyya
Nov 20 '18 at 15:17
2
What phenomenon did you come across?
– Arthur
Nov 20 '18 at 15:19
Your condition is: $ $ equal sum $Rightarrow$ equal product, correct?
– Bill Dubuque
Nov 20 '18 at 15:27
@BillDubuque: Yes, that would be an equivalent formulation.
– EulerSpoiler
Nov 20 '18 at 16:33
add a comment |
Given numbers $a, b, c,; text{and}; d$ (not necessarily distinct), what phenomena is the condition $(ab = cd ; text{or} ; a + b neq c + d)$ linked to? I came across one, but I wanted to see if there were any others before revealing it.
algebra-precalculus
edited Nov 20 '18 at 23:11
user376343
2,8582823
asked Nov 20 '18 at 15:10
EulerSpoiler
729
Given numbers $a, b, c,; text{and}; d$ (not necessarily distinct), what phenomena is the condition $(ab = cd ; text{or} ; a + b neq c + d)$ linked to? I came across one, but I wanted to see if there were any others before revealing it.
algebra-precalculus
algebra-precalculus
edited Nov 20 '18 at 23:11
user376343
2,8582823
asked Nov 20 '18 at 15:10
EulerSpoiler
729
edited Nov 20 '18 at 23:11
user376343
2,8582823
asked Nov 20 '18 at 15:10
EulerSpoiler
729
edited Nov 20 '18 at 23:11
user376343
2,8582823
edited Nov 20 '18 at 23:11
user376343
2,8582823
edited Nov 20 '18 at 23:11
user376343
2,8582823
2,8582823
asked Nov 20 '18 at 15:10
EulerSpoiler
729
asked Nov 20 '18 at 15:10
EulerSpoiler
729
asked Nov 20 '18 at 15:10
EulerSpoiler
729
729
2
Please explain "I came accross one". Provide the proof here please.
– Sujit Bhattacharyya
Nov 20 '18 at 15:17
2
What phenomenon did you come across?
– Arthur
Nov 20 '18 at 15:19
Your condition is: $ $ equal sum $Rightarrow$ equal product, correct?
– Bill Dubuque
Nov 20 '18 at 15:27
@BillDubuque: Yes, that would be an equivalent formulation.
– EulerSpoiler
Nov 20 '18 at 16:33
add a comment |
2
Please explain "I came accross one". Provide the proof here please.
– Sujit Bhattacharyya
Nov 20 '18 at 15:17
2
What phenomenon did you come across?
– Arthur
Nov 20 '18 at 15:19
Your condition is: $ $ equal sum $Rightarrow$ equal product, correct?
– Bill Dubuque
Nov 20 '18 at 15:27
@BillDubuque: Yes, that would be an equivalent formulation.
– EulerSpoiler
Nov 20 '18 at 16:33
2
2
Please explain "I came accross one". Provide the proof here please.
– Sujit Bhattacharyya
Nov 20 '18 at 15:17
Please explain "I came accross one". Provide the proof here please.
– Sujit Bhattacharyya
Nov 20 '18 at 15:17
2
2
What phenomenon did you come across?
– Arthur
Nov 20 '18 at 15:19
What phenomenon did you come across?
– Arthur
Nov 20 '18 at 15:19
Your condition is: $ $ equal sum $Rightarrow$ equal product, correct?
– Bill Dubuque
Nov 20 '18 at 15:27
Your condition is: $ $ equal sum $Rightarrow$ equal product, correct?
– Bill Dubuque
Nov 20 '18 at 15:27
@BillDubuque: Yes, that would be an equivalent formulation.
– EulerSpoiler
Nov 20 '18 at 16:33
@BillDubuque: Yes, that would be an equivalent formulation.
– EulerSpoiler
Nov 20 '18 at 16:33
add a comment |
1 Answer
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Given constants a, b, c, and d, then the equation (x – a)(x – b) = (x – c)(x – d) has a nonempty solution set if, and only if, ab = cd or a + b != c + d.
answered Nov 22 '18 at 3:48
EulerSpoiler
729
add a comment |
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1 Answer
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1 Answer
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active
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active
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votes
Given constants a, b, c, and d, then the equation (x – a)(x – b) = (x – c)(x – d) has a nonempty solution set if, and only if, ab = cd or a + b != c + d.
answered Nov 22 '18 at 3:48
EulerSpoiler
729
add a comment |
Given constants a, b, c, and d, then the equation (x – a)(x – b) = (x – c)(x – d) has a nonempty solution set if, and only if, ab = cd or a + b != c + d.
answered Nov 22 '18 at 3:48
EulerSpoiler
729
add a comment |
Given constants a, b, c, and d, then the equation (x – a)(x – b) = (x – c)(x – d) has a nonempty solution set if, and only if, ab = cd or a + b != c + d.
answered Nov 22 '18 at 3:48
EulerSpoiler
729
Given constants a, b, c, and d, then the equation (x – a)(x – b) = (x – c)(x – d) has a nonempty solution set if, and only if, ab = cd or a + b != c + d.
answered Nov 22 '18 at 3:48
EulerSpoiler
729
answered Nov 22 '18 at 3:48
EulerSpoiler
729
answered Nov 22 '18 at 3:48
EulerSpoiler
729
answered Nov 22 '18 at 3:48
EulerSpoiler
729
729
add a comment |
add a comment |
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2
Please explain "I came accross one". Provide the proof here please.
– Sujit Bhattacharyya
Nov 20 '18 at 15:17
2
What phenomenon did you come across?
– Arthur
Nov 20 '18 at 15:19
Your condition is: $ $ equal sum $Rightarrow$ equal product, correct?
– Bill Dubuque
Nov 20 '18 at 15:27
@BillDubuque: Yes, that would be an equivalent formulation.
– EulerSpoiler
Nov 20 '18 at 16:33