If mx^m– nxⁿ = 0, then what is the value of \(\frac{1}{{{x^m} + {x^n}}} + \frac{1}{{{x^m} - {x^n}}}\) terms of xⁿ is:

Where x, m, n are > 0

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 4)

Answer 1

Given:

mxm - nxn =0

Calculation

mxm - nxn =0

mxm = nxn

\(\frac{m}{n} = \frac{x^n}{x^m}\)

so, m = xn and n = xm

\(\frac{1}{{{x^m} + {x^n}}} + \frac{1}{{{x^m} - {x^n}}}\)

Substitute the values

\(\frac{1}{{{n} + {m}}} + \frac{1}{{{n} - {m}}}\)

⇒ \(\frac{2n}{n^2 - m^2}\)

Multiply and Divide the expression by xn

⇒ \(\frac{2n}{n^2 - m^2}\times \frac{x^n}{x^n}\)

Now substitute m = xⁿ in the numerator

⇒ \(\frac{2mn}{x^n(n^2 - m^2)}\)

∴ Option 4 is the correct answer.

Download Solution PDF