If $${x^4} + \frac{1}{{{x^4}}} = \frac{{257}}{{16}},$$ then find $$\frac{8}{{13}}\left( {{x^3} + \frac{1}{{{x^3}}}} \right),$$ where x > 0.
A. 5
B. 4
C. 6
D. 8
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {x^4} + \frac{1}{{{x^4}}} = \frac{{257}}{{16}} \cr & {\left( {{x^2} + \frac{1}{{{x^2}}}} \right)^2} = \frac{{257}}{{16}} + 2 \cr & {\left( {{x^2} + \frac{1}{{{x^2}}}} \right)^2} = {\left( {\frac{{17}}{4}} \right)^2} \cr & {x^2} + \frac{1}{{{x^2}}} = \frac{{17}}{4} \cr & x + \frac{1}{x} = {\left( {\frac{{17}}{4} + 2} \right)^{\frac{1}{2}}} = \frac{5}{2} \cr & {\text{Here }}x = 2 \cr & {\text{Hence }}\frac{8}{{13}}\left( {{x^3} + \frac{1}{{{x^3}}}} \right) \cr & = \frac{8}{{13}}\left( {8 + \frac{1}{8}} \right) \cr & = \frac{8}{{13}} \times \frac{{65}}{8} \cr & = 5 \cr} $$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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