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प्रश्न
Find the value of the following expression: 16x2 + 24x + 9, when \[x = \frac{7}{4}\]
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उत्तर
Let us consider the following expression: \[16 x^2 + 24x + 9\]
Now \[16 x^2 + 24x + 9 = \left( 4x + 3 \right)^2\] (Using identity \[\left( a + b \right)^2 = a^2 + 2ab + b^2\])
\[\Rightarrow 16 x^2 + 24x + 9 = \left( 4 \times \frac{7}{4} + 3 \right)^2 (\text { Substituting } x = \frac{7}{4})\]
\[ \Rightarrow 16 x^2 + 24x + 9 = \left( 7 + 3 \right)^2 \]
\[ \Rightarrow 16 x^2 + 24x + 9 = {10}^2 \]
\[ \Rightarrow 16 x^2 + 24x + 9 = 100\]
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