Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.
Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.
I have tried to approach this by proving the contrapositive instead, but I'm not sure if that's the best approach to this.
proof-writing
asked Dec 6 at 22:19
hunnybuns
305
add a comment |
Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.
I have tried to approach this by proving the contrapositive instead, but I'm not sure if that's the best approach to this.
proof-writing
asked Dec 6 at 22:19
hunnybuns
305
add a comment |
Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.
I have tried to approach this by proving the contrapositive instead, but I'm not sure if that's the best approach to this.
proof-writing
asked Dec 6 at 22:19
hunnybuns
305
Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.
I have tried to approach this by proving the contrapositive instead, but I'm not sure if that's the best approach to this.
proof-writing
proof-writing
asked Dec 6 at 22:19
hunnybuns
305
asked Dec 6 at 22:19
hunnybuns
305
asked Dec 6 at 22:19
hunnybuns
305
asked Dec 6 at 22:19
hunnybuns
305
asked Dec 6 at 22:19
hunnybuns
305
305
add a comment |
add a comment |
2 Answers
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Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
add a comment |
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 at 22:22
Botond
5,4332732
add a comment |
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2 Answers
2
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2 Answers
2
active
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active
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Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
add a comment |
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
add a comment |
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
answered Dec 6 at 22:21
Dietrich Burde
77.3k64386
77.3k64386
add a comment |
add a comment |
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 at 22:22
Botond
5,4332732
add a comment |
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 at 22:22
Botond
5,4332732
add a comment |
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 at 22:22
Botond
5,4332732
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 at 22:22
Botond
5,4332732
answered Dec 6 at 22:22
Botond
5,4332732
answered Dec 6 at 22:22
Botond
5,4332732
answered Dec 6 at 22:22
Botond
5,4332732
5,4332732
add a comment |
add a comment |
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