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Conditional Identities

If x2+1 / x2=...

Question

If x²+1/x²= 7, then find x³+1/x³.
How to do this sum?

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Solution

(x + 1/x)2 = x2 + 1/x2 + 2
given x2+1/x2=7
then

(x + 1/x)2 = 9

x + 1/x = 3

now

(x + 1/x)3 = x3 + 1/x3 + 3(x + 1/x)

27 = x3 + 1/x3 + 9

or

x3 + 1/x3 = 27 - 9 = 18

it shoul be the answer

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Similar questions

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

find the value of

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

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

then the vaue of

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

x \neq - 1

, then find the equation of

\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1} = 1

x \neq - 1

, then find the quotient of

\frac{x^{5} + x^{4} + x^{3} + x^{2}}{x^{3} + x^{2} + x + 1}

If x + (1/x) = 3, find x² + (1/x²) and x³ + (1/x³)

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