Test Index

TANCET 2023 Solved Papers

Question : 59 of 100

Marks: +1, -0

4 x^{4}=7 x^{2}-1

\left(2 x^{2}-\sqrt{3 x}-5\right)

Solution:

Concept:

Rewrite the given quartic equation as a perfect square to simplify the required expression.

Explanation:

Given:

4x^{4}=7x^{2}-1

Rearrange the equation:

4x^{4}-4x^{2}+1=3x^{2}

The left-hand side is a perfect square:

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

Taking the positive square root:

2x^{2}-1=\sqrt{3}\,x

So,

2x^{2}-\sqrt{3}\,x=1

Now substitute into the required expression:

2x^{2}-\sqrt{3}\,x-5=1-5=-4

Answer:

-4

, i.e. Option A

Go to Question:

Prev Question

Next Question