Question

Answer to my question and I will donate 50 points​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :}}}}$

$\boxed{{x}^{2} - \frac{1}{{x}^{2}} = - 24\sqrt{2}}$

$\mathfrak{\large{\underline{\underline{Explanation :}}}}$

Refer to the attachment.

$\textbf{\large{\underline{\underline{Algebraic Identities used :}}}}$

(x + y)² = x² + 2xy + y²

(x + y)(x - y) = x² - y²

$\textsf{\large{\underline{\underline{Additional Information :}}}}$

• An Algebraic identity is an equation, which is true for all values of the variables in the equation.

1) (x + y)² = x² + 2xy + y²

2) (x - y)² = x² - 2xy - y²

3) (x + y)(x - y) = x² - y²

4) (x + a)(x + b) = x² + (a + b)x + ab

5) (x + y)³ = x³ + 3x²y + 3xy² + y³

6) (x - y)³ = x³ - 3x²y + 3xy² - y³

7) x³ + y³ = (x + y)(x² - xy + y²)

8) x³ - y³ = (x - y)(x² + xy + y²)

9) (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz

10) x³ + y³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - xz

• If the product of two two irrational numbers is rational number then each of the two is the Rationalising factor of the other.