Question

if x2+1/x2=142 find value of x3+1/x3

Answer 1

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Answer 2

Answer:

Required answer is 1692

Step-by-step explanation:

Given,

${x}^{2} + \frac{1}{ {x}^{2} } = 142$

${(x + \frac{1}{x} )}^{2} - 2 \times x \times \frac{1}{x} = 142$

${(x + \frac{1}{x} )}^{2} - 2 \ = 142$

${(x + \frac{1}{x} )}^{2} = 142 + 2$

${(x + \frac{1}{x} )}^{2} = 144$

${(x + \frac{1}{x} )} = \sqrt{144}$

${(x + \frac{1}{x} )} = 12$

Now,

${x}^{3} + \frac{1}{ {x}^{3} } = {(x + \frac{1}{x} })^{3} - 3x \times \frac{1}{x} (x + \frac{1}{x} )$

${x}^{3} + \frac{1}{ {x}^{3} } = {12}^{3} - 3 \times 12 = 1728 - 36 = 1692$