Question

If x + $\frac{1}{x}$= 5, then $\left( x^{3} + \frac{1}{x^{3}} \right)$– 5 $\left( x^{2} + \frac{1}{x^{2}} \right)$+ $\left( x + \frac{1}{x} \right)$is equal to

• A. 0
• B. 5
• C. –5
• D. 10

Answer 1

Answer: (A)

0

Answer 2

= $\left( x + \frac{1}{x} \right)^{3}$– 3 $\left( x + \frac{1}{x} \right)$– 5$\left\lbrack \left( x + \frac{1}{x} \right)^{2} - 2 \right\rbrack$+ $\left( x + \frac{1}{x} \right)$

= $\left( x + \frac{1}{x} \right)^{3}$– 5 $\left( x + \frac{1}{x} \right)^{2}$– 2 $\left( x + \frac{1}{x} \right)$+ 10

= 125 – 125 – 2 × 5 + 10 = 0