Question

Solve:
squareroot 2x-1 - squareroot x+3 = 1

please show steps

Answer 1

sqrt(2x-1) - sqrt(x+3) = 1

We're gonna have to square things twice

(2x-1) - 2sqrt(2x-1)(x+3) + (x+3) = 1
3x+2 - 2sqrt(2x-1)(x+3) = 1
2sqrt(2x-1)(x+3) = -3x - 1
4(2x-1)(x+3) = (-3x-1)^2
8x^2 + 20x - 12 = 9x^2 + 6x + 1
x^2 - 14x + 13 = 0
(x-13)(x-1) = 0

so x=13 or x=1

But, with all that squaring, wde may have introduced spurious root. So, check in the original equation:

sqrt(2x-1) - sqrt(x+3) = 1
x=13
sqrt(25) - sqrt(16) = 1 YES!
sqrt(-1) - sqrt(4) = 1 NOPE!

Looks like 13 is the answer