Question

if x^2+1/x^2=34 then find the value of x^3+1/x^3 please tell fast​

Answer 1

Given :

$\\ \red \bigstar \tt \: \frac{ {x}^{2} + 1}{ {x}^{2} } = 34$

To Find :

$\\ \pink\bigstar\tt { \dfrac{x^{3}+1}{x^{3}}=?}$

Solution :

By using square formula :

$\\ \implies \sf \: { \bigg( \frac{x + 1}{x} \bigg) }^{2} = \bigg( \frac{ {x}^{2} + 1}{ {x}^{2} + 2} \bigg) \\ \\ \implies \sf \bigg( { \frac{x + 1}{x} } \bigg)^{2} = 34 + 2 \\ \\ \implies \sf \bigg( { \frac{x + 1}{x} } \bigg)^{2} = 36 \\ \\ \implies \boxed{ \sf{ \bigg( \frac{x + 1}{x} \bigg) = 6}}$

Now, by using cubic formula :

$\\ \implies \sf \: \bigg( { \frac{x + 1}{x} } \bigg)^{3} = \bigg( {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times x \times \frac{1}{x} \bigg) \\ \\ \implies \sf \: {6}^{3} - 3(6) = \bigg( {x}^{3} + \frac{1}{ {x}^{3} } \bigg) \\ \\ \implies \sf \: 216 - 18 = \bigg( {x}^{3} + \frac{1}{ {x}^{3} } \bigg) \\ \\ \implies \boxed{ \sf{ \bigg( {x}^{3} + \frac{1}{ {x}^{3} } \bigg) = 198}}$

The correct answer will be 198