Question

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

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\boxed{\sf{Formula\:used=(a+b){}^{3}}}$

• Where in the place of a =x

• And place of b=$\sf \frac{1}{x}$

Now :-

$\tt\implies (x+\frac{1}{x}){}^{3}=x{}^{3}+\frac{1}{x{}^{3}}+3\times \cancel{x}\times \frac{1}{\cancel{x}} (x+\frac{1}{x})\\ \\ \tt\implies [x+\frac{1}{x}]{}^{3}=x{}^{3}+\frac{1}{x{}^{3}}+3(x+\frac{1}{x})$

$\bf\underline{According\:To\: Question:-}$

$\sf\implies [x+\frac{1}{x}]{}^{3}=x{}^{3}+\frac{1}{x{}^{3}}+3(x+\frac{1}{x})\\ \\ \sf\implies (5){}^{3}=x{}^{3}+\frac{1}{x{}^{3}}+3\times 5\\ \\ \sf\implies 125=x{}^{3}+\frac{1}{x{}^{3}}+15\\ \\ \sf\implies 125-15=x{}^{3}+\frac{1}{x{}^{3}}\\ \\ \sf\implies x{}^{3}+\frac{1}{x{}^{3}}=110$

$\underline{\boxed{\mathfrak{x{}^{3}+\frac{1}{x{}^{3}}=110}}}$