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SSC CGL 2022 PYQ — Question 56

SSC CGL - 05 Dec 2022 - Shift 2 • Quantitative Aptitude • Q56

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If 1x2+a2=x2−a2\frac{1}{x^2+a^2}=x^2-a^2 then find the value of x.

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. (a4 + 1)1/4.

Given:

1(x2+a2)=(x2−a2){1 \over (x^2 + a^2)} = (x^2 - a^2)

Concept Used:

(a + b)(a - b) = a2 - b2

Explanation:

1(x2+a2)=(x2−a2){1 \over (x^2 + a^2)} = (x^2 - a^2)

⇒ (x2 + a2)(x2 - a2) = 1

⇒ x4 - a4 = 1

⇒ x4 = 1 + a4 

⇒ x = (1+a4)1/4(1 + a^4)^{1/4}

Hence the value of x is (1+a4)1/4(1 + a^4)^{1/4}.