The number that is to be added to $x^{2} + 6 x$ to make the resultant a perfect square is _____.

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Solution

The correct option is C 9
Consider the expression $x^{2} + 6 x .$

$\Rightarrow x^{2} + 2 \times x \times 3$

It is in the form of $a^{2} + 2 a b$

By adding $b^{2}$ we get the identity
$a^{2} + 2 a b + b^{2} = (a + b)^{2}$ that represents a perfect square.

$\Rightarrow x^{2} + 2 (x) (3) + 3^{2}$
$= (x + 3)^{2} = x^{2} + 6 x + 9$
is a perfect square.

Thus, we have to add 9 to the expression $x^{2} + 6 x$ so that the resultant is a perfect square.

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