Question

please give in full method​

Answer 1

Qᴜᴇsᴛɪᴏɴ :-

Solve for x :- {√(x+1) + √(x-1)}/{√(x+1) - √(x-1)} = (4x - 1)/2

Sᴏʟᴜᴛɪᴏɴ :-

→ {√(x+1) + √(x-1)}/{√(x+1) - √(x-1)} = (4x - 1)/2

Using C & D , we get,

→ √(x + 1) /√(x - 1) = (4x - 1 + 2) / (4x - 1 - 2)

→ √(x + 1) /√(x - 1) = (4x + 1) / (4x - 3)

Squaring Both Sides Now, we get,

→ (x + 1) / (x - 1) = (4x + 1)²/(4x - 3)²

→ (x + 1) /(x - 1) = (16x² + 8x + 1) / (16x² - 24x + 9)

Cross - Multiply,

→ (x+1)(16x²-24x+9) = (x-1)(16x²+8x+1)

→ 16x³- 24x²+9x + 16x²-24x+9 = 16x³+8x²+x - 16x² - 8x - 1

→ 16x³ - 8x² - 15x + 9 = 16x³ - 8x² - 7x - 1

16x³ - 8x² will be cancel from both sides,

→ - 15x + 9 = - 7x - 1

→ - 7x + 15x = 9 + 1

→ 8x = 10

→ x = (10/8)

→ x = (5/4) (Ans.)