If $${x^2} + \frac{1}{{{x^2}}} = 98{\text{,}}$$ $$\left( {x > 0} \right){\text{,}}$$ then the value of $$x^3 + \frac{1}{{{x^3}}}$$ is?
A. 970
B. 1030
C. -970
D. -1030
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {x^2} + \frac{1}{{{x^2}}} = 98 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 100 \cr & \Rightarrow {\left( {x + \frac{1}{x}} \right)^2} = 100 \cr & \Rightarrow x + \frac{1}{x} = 10 \cr & {\text{Cubing}}\,{\text{both}}\,{\text{sides}} \cr & \Rightarrow {\text{ }}{x^3} + \frac{1}{{{x^3}}} = {10^3} - 3 \times 10 \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 1000 - 3 \times 10 \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 970 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
Join The Discussion