If $2x^2 - 6x = 1,$ then $x^2 + \frac{1}

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $2x^2 - 6x = 1,$ then $x^2 + \frac{1}{4x^2} = ?$

Options:

Correct Answer:

Explanation:

We know that,

If $K-\frac{1}{K}=n$

then, $K^2+\frac{1}{K^2}$ = n² + 2

If $2x^2 - 6x = 1,$

$x^2 + \frac{1}{4x^2} = ?$

Divide both sides by 2x on If $2x^2 - 6x = 1,$ we get,

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

and $x^2 + \frac{1}{4x^2}$ = 3² + 2 × $\frac{1}{2}$ = 9 + 1 = 10