If x²+1/x²=23, find the value of x³-1/x³. (plzz slove it out)
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x² + 1/x² = 23
Add 2 on both sides,
x² + 1/x² + 2 = 25
( x + 1/x)² = 25²
( x +1/x) = 5
We know that,
(x³ + 1/x³ ) = (x+1/x)³ - 3x(1/x)( x + 1/x)
x³ + 1/x³ = 5³ -3 (5)
x³ + 1/x³ = 125 - 15 = 110
Add 2 on both sides,
x² + 1/x² + 2 = 25
( x + 1/x)² = 25²
( x +1/x) = 5
We know that,
(x³ + 1/x³ ) = (x+1/x)³ - 3x(1/x)( x + 1/x)
x³ + 1/x³ = 5³ -3 (5)
x³ + 1/x³ = 125 - 15 = 110
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