यदि \(\rm \frac{1}{x^2+a^2}\)= x2 - aहै, तो x का मान है:

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 2)
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  1. (1 - a4)1/4
  2. a
  3. (a4 - 1)1/4
  4. (a4 + 1)1/4

Answer (Detailed Solution Below)

Option 4 : (a4 + 1)1/4
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Detailed Solution

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दिया गया है:

\(\rm \frac{1}{x^2+a^2}\)= x2 - a2

प्रयुक्त अवधारणा:

a2 - b2 = (a + b)(a - b)

गणना:

\(\rm \frac{1}{x^2+a^2}\)= x2 - a2

⇒ (x2 - a2)(x2 + a2) = 1

⇒ x4 - a4 = 1

⇒ x4 =  1 + a4

⇒ x = (a4 + 1)1/4

∴ x का मान ​(a4 + 1)1/4 है।

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