Question

Please anyone help..I want step-by-step solution..​

Answer 1

Answer:

Given:

• 2x = a + 1/a ⇒ x = 1/2(a + 1/a)
• 2y = b + 1/b ⇒ y = 1/2(b + 1/b)

Find xy:

• xy = 1/2(a + 1/a)*1/2(b + 1/b) = 1/4(ab + 1/ab + a/b + b/a)

Find x²:

• x² = [1/2(a + 1/a)]² = 1/4(a² + 1/a² + 2) = 1/4(a² + 1/a² - 2 + 4) = 1/4(a- 1/a)²  + 1 ⇒ x² - 1 = [1/2(a - 1/a)]² ⇒ $\sqrt{x^2-1}$ = 1/2(a - 1/a)

Similarly to above:

• $\sqrt{y^2-1}$ = 1/2(b - 1/b)

Simplify left side of equation:

• 1/4(ab + 1/ab + a/b + b/a) + 1/2(a - 1/a)*1/2(b - 1/b) =
• 1/4(ab + 1/ab + a/b + b/a) + 1/4(ab + 1/ab - a/b - b/a) =
• 1/4(2ab + 2/ab) =
• 1/2(ab + 1/ab)

We got the right side, so proved the equation.