The sum of $a$ and $b$ is $132$ . If $a$ is the square of $b$ and the product of $a$ and $b$ is negative, what is $a$ ?

-12

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121

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144

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Solution

The correct option is C 144
Sum of $a$ and $b$ is $132$ .
$\Rightarrow a + b = 132$
$a$ is square of $b$
$\Rightarrow a = b^{2}$

Substituting above, we get
$b^{2} + b = 132$
$\Rightarrow b^{2} + b - 132 = 0$
$\Rightarrow (b + 12) (b - 11) = 0$
$\Rightarrow b = - 12$ . since product of $a$ and $b$ is negative.
Then $a = b^{2} = {(- 12)}^{2} = 144$

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The sum of a and b is 132. If a is the square of b and the product of a and b is negative, what is a?

The correct option is C 144Sum of a and b is 132.⇒a+b=132a is square of b⇒a=b2Substituting above, we getb2+b=132⇒b2+b−132=0⇒(b+12)(b−11)=0⇒b=−12. since product of a and b is negative.Then a=b2=(−12)2=144

The sum of $a$ and $b$ is $132$ . If $a$ is the square of $b$ and the product of $a$ and $b$ is negative, what is $a$ ?