If $$x + \frac{1}{x} = 5,$$ then what is the value of $${x^6} + \frac{1}{{{x^6}}}?$$
A. 623
B. 627
C. 12098
D. 12012
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & x + \frac{1}{x} = 5 \cr & {\text{Cubing both sides, we get}} \cr & {x^3} + \frac{1}{{{x^3}}} + 3 \times x \times \frac{1}{x}\left( {x + \frac{1}{x}} \right) = 125 \cr & {x^3} + \frac{1}{{{x^3}}} + 3 \times 5 = 125 \cr & {x^3} + \frac{1}{{{x^3}}} = 110 \cr & {\text{Squaring both sides, we get}} \cr & {x^6} + \frac{1}{{{x^6}}} + 2 = 12100 \cr & {x^6} + \frac{1}{{{x^6}}} = 12098 \cr} $$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. $$\frac{8}{6}$$
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