Question 19

What number must be added to the expression $$16a^2 - 12a$$ to make it a perfect square?

Solution

$$16a^2 - 12a$$ = $$\left(4a\right)^2-\left(2\right)\left(4a\right)\left(\ \frac{\ 3}{2}\right)$$

by adding $$\left(\ \frac{\ 3}{2}\right)^2\ $$ we can write it as $$\left(\ 4a-\frac{\ 3}{2}\right)^2\ $$

Hence $$\left(\frac{\ 3}{2}\right)^2\ =\ \ \frac{\ 9}{4}$$ is required answer

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