If x2 - √7x + 1 = 0, then what is the value of $${x^5} + \frac{1}{{{x^5}}}?$$
A. 19√7
B. 25√7
C. 27√7
D. 21√7
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {x^2} - \sqrt 7 x + 1 = 0 \cr & {x^2} + 1 = \sqrt 7 x \cr & x + \frac{1}{x} = \sqrt 7 \cr & {x^5} + \frac{1}{{{x^5}}} = \left( {{x^2} + \frac{1}{{{x^2}}}} \right)\left( {{x^3} + \frac{1}{{{x^3}}}} \right) - \left( {x + \frac{1}{x}} \right) \cr & = \left( {{{\left( {\sqrt 7 } \right)}^2} - 2} \right)\left( {{{\left( {\sqrt 7 } \right)}^3} - 3 \times \sqrt 7 } \right) - \sqrt 7 \cr & = 5 \times 4\sqrt 7 - \sqrt 7 \cr & = 19\sqrt 7 \cr} $$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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