Question 30525
sqrt(2x+5) + sqrt(x+6) = 9
sqrt(2x+5)= 9 - sqrt(x+6) ...square both sides
2X+5=81+X+6-18*SQRT.(X+6)
X-82 = -18*SQRT.(X+6)...SQUARING AGAIN
X^2+6724-164X =324(X+6)=324X+1944
X^2- 488X+4780 = 0
X^2-10X - 478X+4780=0
X(X-10)- 478(X - 10)=0
(X-10)(X-478)=0...HENCE X-10 = 0 ....OR....X=10 WHICH IS CORRECT  SINCE 
sqrt(2x+5) + sqrt(x+6) =sqrt(2*10+5) + sqrt(10+6) = 5 + 4 = 9
X-478 = 0 OR ..X=478 IS AN EXTRANEOUS ANSWER OBTAINED DUE TO REPEATED SQUARING ...WE SHOULD IGNORE THAT