# Solve for x: sqrt(x^2+x-6)-x+2 = sqrt(x^2-7x+10) x is a rational no.. Plz answer fast.

Hence problem is

{(x+3)(x-2)}

^{1/2 }-(x-2) = {(x-2)(x-5)}

^{1/2 }

Taking (x -2)

^{1/2}as common factor and cancelling on both sides we have

(x+3)

^{1/2}- (x-2)

^{1/2}= (x-5)

^{1/2 }

Squaring on both sides, (x+3) +(x+2) - 2 {(x+3)(x-2)}

^{1/2 }= x - 5

2x + 5 - 2{(x+3)(x-2)}

^{1/2 }= x - 5

x + 10 = 2{(x+3)(x-2)}

^{1/2 }

Squaring x^2 + 20x + 100 = 4 (x^2 + x -6)

Or 3x^2 - 16 x - 124 = 0

The descriminant is not a perfect square. So as x has to be a rational number, the common factor taken out and canclled out namely (x -2)

^{1/2}= 0

===>

**x = 2**