if x^2+1/x^2=23 find the value of x^3-1/x^3=110
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Given,
x² + 1/x² = 23
=> (x - 1/x)² + 2 = 23
=> x - 1/x = √21
Now,
x³ - 1/x³ = (x - 1/x)(x² + 1 + 1/x²)
=> x³ - 1/x³ = (√21)(23 + 1) = 24√21
Hope It Helps!
x² + 1/x² = 23
=> (x - 1/x)² + 2 = 23
=> x - 1/x = √21
Now,
x³ - 1/x³ = (x - 1/x)(x² + 1 + 1/x²)
=> x³ - 1/x³ = (√21)(23 + 1) = 24√21
Hope It Helps!
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