If x2 - 5x + 1 = 0, then the value of $$\left( {{x^4} + \frac{1}{{{x^2}}}} \right) \div \left( {{x^2} + 1} \right)$$ is:
A. 21
B. 22
C. 25
D. 24
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {x^2} - 5x + 1 = 0 \cr & \left( {{x^4} + \frac{1}{{{x^2}}}} \right) \div \left( {{x^2} + 1} \right) = ? \cr & {x^2} - 5x + 1 = 0 \cr & \Rightarrow x + \frac{1}{x} = 5 \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = 110 \cr & \frac{{x\left( {{x^3} + \frac{1}{{{x^3}}}} \right)}}{{x\left( {x + \frac{1}{x}} \right)}} = \frac{{110}}{5} = 22 \cr} $$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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