If $a + b = 8$ $a + b = 8$ and $a^{2} + b^{2} = 60$ $a^2 + b^2 = 60$ , what is $a^{2} b^{2}$ $a^2b^2$ ?

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If $a + b = 8$ $a + b = 8$ and $a^{2} + b^{2} = 60$ $a^2 + b^2 = 60$ , what is $a^{2} b^{2}$ $a^2b^2$ ?

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Answer 1 · 2018-02-08T07:50:05

The answer is $= 4$ $=4$

Explanation:

$(a + b) = 8$ $(a+b)=8$

and

$a^{2} + b^{2} = 60$ $a^2+b^2=60$

Therefore,

${(a + b)}^{2} = 8^{2} = 64$ $(a+b)^2=8^2=64$

But,

${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$ $(a+b)^2=a^2+b^2+2ab$

So,

$64 = 60 + 2 a b$ $64=60+2ab$

$2 a b = 64 - 60 = 4$ $2ab=64-60=4$

$a b = \frac{4}{2} = 2$ $ab=4/2=2$

and

$a^{2} b^{2} = {(a b)}^{2} = 2^{2} = 4$ $a^2b^2=(ab)^2=2^2=4$

Answer 2 · 2018-02-08T11:30:11

$a^{2} b^{2} = 4$ $a^2b^2=4$

Explanation:

$given a + b = 8$ $"given "a+b=8$

$then {(a + b)}^{2} = 8^{2} = 64$ $"then "(a+b)^2=8^2=64$

$now {(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $"now "(a+b)^2=a^2+2ab+b^2$

$\Rightarrow a^{2} + 2 a b + b^{2} = 64$ $rArra^2+2ab+b^2=64$

$substitute a^{2} + b^{2} = 60$ $"substitute "a^2+b^2=60$

$\Rightarrow 60 + 2 a b = 64$ $rArr60+2ab=64$

$\Rightarrow 2 a b = 64 - 60 = 4$ $rArr2ab=64-60=4$

$\Rightarrow a b = \frac{4}{2} = 2$ $rArrab=4/2=2$

$square both sides$ $color(blue)"square both sides"$

$\Rightarrow {(a b)}^{2} = 2^{2}$ $rArr(ab)^2=2^2$

$\Rightarrow a^{2} b^{2} = 4$ $rArra^2b^2=4$

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If $a + b = 8$ $a + b = 8$ and $a^{2} + b^{2} = 60$ $a^2 + b^2 = 60$ , what is $a^{2} b^{2}$ $a^2b^2$ ?

2 Answers

Explanation:

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If a+b=8a + b = 8 and a2+b2=60a^2 + b^2 = 60, what is a2b2a^2b^2 ?

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Explanation:

Explanation:

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If $a + b = 8$ $a + b = 8$ and $a^{2} + b^{2} = 60$ $a^2 + b^2 = 60$ , what is $a^{2} b^{2}$ $a^2b^2$ ?