Let $a$ and $b$ be two integers. Prove that if $ab=4$, then $(a-b)^3-9(a-b)=0$.
$begingroup$
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 '18 at 22:19
hunnybunshunnybuns
15
$endgroup$
add a comment |
$begingroup$
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 '18 at 22:19
hunnybunshunnybuns
15
$endgroup$
add a comment |
$begingroup$
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 '18 at 22:19
hunnybunshunnybuns
15
$endgroup$
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 '18 at 22:19
hunnybunshunnybuns
15
asked Dec 6 '18 at 22:19
hunnybunshunnybuns
15
asked Dec 6 '18 at 22:19
hunnybunshunnybuns
15
asked Dec 6 '18 at 22:19
hunnybunshunnybuns
15
asked Dec 6 '18 at 22:19
hunnybunshunnybuns
15
15
add a comment |
add a comment |
2 Answers
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$begingroup$
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
$endgroup$
add a comment |
$begingroup$
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
$endgroup$
add a comment |
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2 Answers
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2 Answers
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$begingroup$
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
$endgroup$
add a comment |
$begingroup$
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
$endgroup$
add a comment |
$begingroup$
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
$endgroup$
Hint: What are the integer solutions of $ab=4$ ?
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
answered Dec 6 '18 at 22:21
Dietrich BurdeDietrich Burde
80.3k647104
80.3k647104
add a comment |
add a comment |
$begingroup$
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
$endgroup$
add a comment |
$begingroup$
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
$endgroup$
add a comment |
$begingroup$
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
$endgroup$
Hint: What values can $a$ and $b$ take? Why don't you substitute them into the lhs?
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
answered Dec 6 '18 at 22:22
BotondBotond
5,9882832
5,9882832
add a comment |
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