Hi! May I know the answer of:
Solve:
sqrt(2 x-6) + sqrt(x+4) = 5.

Here, sqrt(2x-6)+sqrt(x+4)=5 Squaring both sides, => 2x-6+x+4+2 sqrt((x+4)(2x-6)) =25 => 3x-2 + 2 sqrt((x+4)(2x-6)) = 25 =>2 sqrt((x+4)(2x-6)) =27-3x Squaring both sides, => 4(x+4)(2x-6)=(27-3x)^2 =>8x^2 + 8x -96 = 9x^2 -162 x +729 => -x^2 + 170x- 825=0 => -(x-165)(x-5)=0 =>(x-165)(x-5)=0 . so x= 165 or x=5.

when x=165 , LHS of question = sqrt(2x-6)+sqrt(x+4) = sqrt(2*165 – 6)+sqrt(4+165) =31 not equal to RHS

 

So x=5. (Ans.)