Question

If (√13+x + √13-x):(√13+x - √13-x)=5 then x is ?​

Answer 1

Step-by-step explanation:

(√13+x + √13-x):(√13+x - √13-x)=5

Multiplying and Dividing the LHS with (√13+x + √13-x)

[(√13+x + √13-x)]² : [(√13+x - √13-x)×(√13+x + √13-x)] = 5

(13+x) + (13-x) + {2•(√13+x)•(√13-x)} : (13+x-13+x) = 5

(a²-b² = (a+b)(a-b))

(26/2x) + [{2•(√13+x)•(√13-x)}/2x] = 5

(√13+x)•(√13-x) = (10x-26)/2

(squaring on both sides)

(13²-x²) = (5x-13)²

169 - x² = 25x² + 169 - (2•5x•13)

-26x² = -130x

x² = 5x

x = 5 (or) x = 0