Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $\frac{1}{x^2+a^2} = x^2 - a^2$, then the value of x is:

Options:

$(1-a^4)^{1/4}$

a

$(a^4-1)^{1/4}$

$(a^4+1)^{1/4}$

Correct Answer:

$(a^4+1)^{1/4}$

Explanation:

If $\frac{1}{x^2+a^2} = x^2 - a^2$

1 = ($x^2 - a^2$) ($x^2 + a^2$)

we know =  a4 – b4 = ($a^2 - b^2$) ($a^2 + b^2$)

x4 – a4 = ($x^2 - a^2$) ($x^2 + a^2$)

x4 – a4 = 1

x4  = 1 + a4

x = $(a^4+1)^{1/4}$