Question

√x+5+√x+21=√6x+40

Answer 1

√(x + 5) + √(x + 21) = √(6x + 40)

=>[√(x + 5) + √(x + 21)]2 = [√(6x + 40)] 2

=> (x + 5)+ (x + 21) + 2√(x+ 5)(x + 21) = 6x + 40



=> √(x+ 5)(x + 21) = 2x + 7

=> (x+ 5)(x + 21) = (2x + 7)2

=> 3x2 + 2x – 56 = 0

=> (3x + 14)(x - 4) = 0

=> x = 4 or x = -14/3.

Clearly, x = -14/3 does not satisfy the given equation. Hence, x = 4 is the only root of the given equation.