If x4 + x-4 = 194, x > 0, then what is the value of $$x + \frac{1}{x} + 2?$$
A. 6
B. 8
C. 4
D. 14
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {x^4} + {x^{ - 4}} = 194 \cr & {\left( {{x^2} + \frac{1}{{{x^2}}}} \right)^2} = 194 + 2 \cr & {\left( {{x^2} + \frac{1}{{{x^2}}}} \right)^2} = 196 \cr & {x^2} + \frac{1}{{{x^2}}} = 14 \cr & x + \frac{1}{x} = {\left( {16} \right)^{\frac{1}{2}}} \cr & x + \frac{1}{x} = 4 \cr & x + \frac{1}{x} + 2 = 4 + 2 \cr & x + \frac{1}{x} = 6 \cr} $$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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