How do you solve:?

Question

square root of 7-x minus square root of 6+x = 1

Thanks

Answer 1

SQRT(7 - x) - SQRT(6 + x) = 1
Everything squared
(7 - x) + (6 + x) - 2SQRT((7 - x)(6+x)) = 1
13 -1 = 2 SQRT((7 - x)(6+x))
6 = SQRT((7 - x)(6+x))
Square again.
36 = (7 - x)(6 + x)
x1 = 3
x2 = -2

Test that x1 and/or x2 solve the original equation.

Answer 2

sqrt(7-x)-sqrt(6+x)=1
squaring both sides
=>7-x+6+x-2sqrt(7-x)sqrt(6+x)=1
=>13=1+2sqrt(7-x)sqrt(6+x)
=>sqrt(7-x)sqrt(6+x)=6
squaring again,
=>(7-x)(6+x)=36
=>42-x*x+x=36
=>x^2-x-6=0
=>(x-3)(x+2)=0
=>x=3,-2

Answer 3

a calculator is your best friend :D