Question

If x - 1/x = 4, then find the value of this x^2 + 1/x^2​

Answer 1

Answer:

Step-by-step explanation:

Given: x - 1/x = 4

Squaring on both sides,

formula of (a-b)^2​ = a^2​ + b^2​ - 2ab

  (x - 1/x)^2​ = (4)^2​

  x^2​ + 1/x^2 - 2*x*1/x = 16

  x^2​ + 1/x^2 - 2 = 16

  x^2​ + 1/x^2  = 16 + 2

  x^2​ + 1/x^2 = 18

Answer: 18

Answer 2

Answer:

The value of x²+1/x² is 18

Step-by-step explanation:

Given that,

$\sf{x - \frac{1}{x} = 4 }$

To find the value of:

$\sf{x {}^{2} + \frac{1}{x {}^{2} } }$

Of the form of the below identity,

(a-b)²=a²-2ab+b²

Here,

$\sf{a = x \: \: and \: \: b = \frac{1}{x} }$

Substituting appropriate values,

$\sf{(x - \frac{1}{x}) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } - 2x. \frac{1}{x} } \\ \\ \implies \: \sf{4 {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } - 2 } \\ \\ \implies \: \sf{x {}^{2} + \frac{1}{x {}^{2} } = 16 + 2 } \\ \\ \implies \: \ \boxed{ \boxed{ \sf{x {}^{2} + \frac{1}{x {}^{2} } = 18 }}}$