Question

If x-1/x = 4 , find the value of x² + 1/x²​

Answer 1

Answer:

8

Step-by-step explanation:

this is the correct answer for this question

Answer 2

GIVEN :–

• x - 1/x = 4

TO FIND :–

• Value of x² + 1/x² = ?

SOLUTION :–

$\\ \bf \implies \: x - \dfrac{1}{x} = 4$

• Square on both sides –

$\\ \bf \implies \: \left(x - \dfrac{1}{x} \right)^{2} = (4)^{2}$

• We know that –

$\\ \bf \pink{\twoheadrightarrow \: \left(a-b\right)^{2} =a^{2} +b^{2} - 2ab}$

• So that –

$\\ \bf \implies \: {x}^{2} + \left( \dfrac{1}{x} \right)^{2} - 2(x) \left(\dfrac{1}{x} \right) = (4)^{2}$

$\\ \bf \implies \: {x}^{2} + \left( \dfrac{1}{x} \right)^{2} - 2= 16$

$\\ \bf \implies \: {x}^{2} + \dfrac{1}{ {x}^{2} } - 2= 16$

$\\ \bf \implies \: {x}^{2} + \dfrac{1}{ {x}^{2} }= 16 + 2$

$\\ \bf \implies \: {x}^{2} + \dfrac{1}{ {x}^{2} }= 18$

• Hence , The value of (x² + 1/x²) is 18.