If $$2x + \frac{2}{x} = 3{\text{,}}$$ then the value of $${x^3} + \frac{1}{{{x^3}}} + 2$$ is?
A. $$ - \frac{9}{8}$$
B. $$ - \frac{{25}}{8}$$
C. $$\frac{7}{8}$$
D. 11
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{ }}2x + \frac{2}{x} = 3 \cr & \Rightarrow {\text{ }}x + \frac{1}{x} = \frac{3}{2} \cr & {\text{Taking cube on both sides}} \cr & \Rightarrow {\left( {x + \frac{1}{x}} \right)^3} = {\left( {\frac{3}{2}} \right)^3}{\text{ }} \cr & x + \frac{1}{x} = a \cr & {x^3} + \frac{1}{{{x^3}}} = {a^3} - 3a \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} + 3\left( {x + \frac{1}{x}} \right) = \frac{{27}}{8} \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} + 3 \times \frac{3}{2} = \frac{{27}}{8} \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = \frac{{27}}{8} - \frac{9}{2} \cr & \Rightarrow {x^3} + \frac{1}{{{x^3}}} = \frac{{ - 9}}{8} \cr & \therefore {x^3} + \frac{1}{{{x^3}}} + 2 \cr & = \frac{{ - 9}}{8} + 2 \cr & = \frac{{ - 9 + 16}}{8} \cr & = \frac{7}{8} \cr} $$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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