Given that x8 - 34x4 + 1 = 0, x > 0, what is the value of (x3 + x-3)?
A. 5√8
B. 5√6
C. 6√8
D. 6√6
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {x^4}\left( {{x^4} - 34 + \frac{1}{{{x^4}}}} \right) = 0 \cr & {x^4} + \frac{1}{{{x^4}}} = 34 \cr & {x^4} + \frac{1}{{{x^4}}} + 2 = 36 \cr & {x^2} + \frac{1}{{{x^2}}} = 6 \cr & x + \frac{1}{x} = \sqrt 8 \cr & {x^3} + \frac{1}{{{x^3}}} = 8\sqrt 8 - 3\sqrt 8 \cr & {x^3} + \frac{1}{{{x^3}}} = 5\sqrt 8 \cr} $$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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