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Find the Value of the Following Expression: 16x2 + 24x + 9, When X = 7 4 - Mathematics

Answer in Brief

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

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Solution

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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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 13.1 | Page 44
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