Question

Please answer this easy algebraic formula :​

Answer 1

Proof :

Given,

{√(1 + x) + √(1 - x)}/{√(1 + x) - √(1 - x)} = p

or, {√(1 + x) + √(1 - x)}²/{(1 + x) - (1 - x)} = p

[ by rationalising the denominator ]

or, {1 + x + 1 - x + 2√(1 - x²)}/(1 + x - 1 + x) = p

or, {2 + 2√(1 - x²)}/(2x) = p

or, 1 + √(1 - x²) = px

or, √(1 - x²) = px - 1

or, 1 - x² = p²x² - 2px + 1

or, p²x² - 2px + x² = 0

or, p² - 2p/x + 1 = 0 [ x ≠ 0 ]

Hence, proved.