Question

Find the value of the following expression: 16x² + 24x + 9, when \[x = \frac{7}{4}\]

Answer 1

Let us consider the following expression: \[16 x^2 + 24x + 9\]

Now \[16 x^2 + 24x + 9 = \left( 4x + 3 \right)^2\]                (Using identity \[\left( a + b \right)^2 = a^2 + 2ab + b^2\])

\[\Rightarrow 16 x^2 + 24x + 9 = \left( 4 \times \frac{7}{4} + 3 \right)^2 (\text { Substituting } x = \frac{7}{4})\]

\[ \Rightarrow 16 x^2 + 24x + 9 = \left( 7 + 3 \right)^2 \]

\[ \Rightarrow 16 x^2 + 24x + 9 = {10}^2 \]

\[ \Rightarrow 16 x^2 + 24x + 9 = 100\]