Question

if x+1/x=5 find the value of x^3+1/x^3​

Answer 1

The first equation given,

x-\frac{1}{x}=5x−x1=5 …….. (i)

If we do the cube of equation (i) we get,

\left(x-\frac{1}{x}\right)^{3}=5^{3}(x−x1)3=53

x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times x \times\left(\frac{1}{x}\right) \times\left(x-\frac{1}{x}\right)=125x3−(x1)3−3×x×(x1)×(x−x1)=125

x^{3}-\left(\frac{1}{x}\right)^{3}-3\times(x-\frac{1}{x})=125x3−(x1)3−3×(x−x1)=125

x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times 5=125x3−(x1)3−3×5=125

Grouping the terms,

x^{3}-\left(\frac{1}{x}\right)^{3}=125+15x3−(x1)3=125+15

x^{3}-\left(\frac{1}{x}\right)^{3}=140x3−(x1)3=140