Question

if x+1/x=7 the find the value of x^3+1/x^3, x^2+1/x^2​

Answer 1

answer is 47

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Answer 2

$x + \frac{1}{x} = 7$

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

${7}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

$49 = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

$49 - 2 = {x}^{2} + \frac{1}{ {x}^{2} }$

$\fbox{ {x}^{2} + \frac{1}{ {x}^{2} } = 47}$

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

${7}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3(7)$

$343 = {x}^{3} + \frac{1}{ {x}^{3} } + 21$

${x}^{3} + \frac{1}{ {x}^{3} } = 343 - 21$

$\fbox{ {x}^{3} + \frac{1}{ {x}^{3} } = 322}$