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CTET Paper II (Mathematics and Science) 9 Jan 2023 Solved Paper

Question : 37 of 150

Marks: +1, -0

3x-\frac{1}{2x}=8

9x^{2}+\frac{1}{4x^{2}}

is:

Solution:

Concept:

Use the algebraic identity

(a - b)^2 = a^2 + b^2 - 2ab

to relate the given expression to the required one.

Explanation:

Square both sides of given equation:

3x - \frac{1}{2x} = 8

\left(3x - \frac{1}{2x}\right)^2 = 8^2 = 64

Expand the left side using the identity:

9x^2 + \frac{1}{4x^2} - 2 \cdot 3x \cdot \frac{1}{2x} = 64

Simplify the product:

2 \cdot 3x \cdot \frac{1}{2x} = 3

. Thus:

9x^2 + \frac{1}{4x^2} - 3 = 64

Add 3 to both sides:

9x^2 + \frac{1}{4x^2} = 67

Answer:

Option D (67).

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