If $$a + \frac{1}{a} = 3,$$ then the value of $${a^3} + \frac{1}{{{a^3}}}$$ is?
A. 27
B. 24
C. 19
D. 18
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{Given , }}a + \frac{1}{a} = 3 \cr & {\text{Cube both sides}} \cr & {a^3} + \frac{1}{{{a^3}}} + 3 \times a \times \frac{1}{a}\left( {a + \frac{1}{a}} \right) = {\left( 3 \right)^3} \cr & \Rightarrow {a^3} + \frac{1}{{{a^3}}} + 3 \times 3 = 27 \cr & \Rightarrow {a^3} + \frac{1}{{{a^3}}} = 27 - 9 \cr & \Rightarrow {a^3} + \frac{1}{{{a^3}}} = 18 \cr} $$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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