Question

Evaluate (x+\frac1x)²+(x²+\frac1x²)²+(x³+\frac1x³)² up to n terms is

• A. \(\dfrac{x^{2n}}{x^2-1}-\dfrac{x^{2n+2}+1}{x^{2n}}+2n\)
• B. \(\dfrac{x^{2n}+1}{x^2+1}\times\dfrac{x^{2n+2}-1}{x^{2n}}-2n\)
• C. \(\dfrac{x^{2n}-1}{x^2-1}\times\dfrac{x^{2n}-1}{x^{2n}}-2n\)
• D. None of these

Hint:

Always expand symmetric expressions using standard identities.

Answer 1

The Correct Option is C

Using identity: (xᵏ+\frac1xᵏ)²=x²k+\frac1x²k+2 Summing and simplifying gives option (c).