Question

x+1/x=10/3, find x^3+1/x^3

Answer 1

Step-by-step explanation:

Given:

$x+\frac{1}{x}=\frac{10}{3}$ -----(i)

Required to Find:

$x^{3}+\frac{1}{x^{3}}$

Solution:

Take cube to both sides of the equation (i),

We get,

$(x+\frac{1}{x})^{3}=(\frac{10}{3})^{3}\\\\=>(x)^{3}+(\frac{1}{x})^{3}+3*x*\frac{1}{x}(x+\frac{1}{x})=\frac{1000}{27}$

[∵ (a + b)³= a³ + b³ + 3ab(a + b)]

$=>x^{3}+\frac{1}{x^{3}}+3*\frac{10}{3}=\frac{1000}{27}\\\\=>x^{3}+\frac{1}{x^{3}}+10=\frac{1000}{27}\\\\=>x^{3}+\frac{1}{x^{3}}=\frac{1000}{27}-10\\\\=>x^{3}+\frac{1}{x^{3}}=\frac{1000-270}{27}\\\\=>x^{3}+\frac{1}{x^{3}}=\frac{730}{27}\\\\=>x^{3}+\frac{1}{x^{3}}=27\frac{1}{27}$

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