Verified answer

(X-3)=SQRT(X+2)-1

Square everyhintg:

x^2-6x+9 = x+2 - 2sqrt(x+2) -1

We know from the start: sqrt(x+2) = x-3 + 1 = x-2

x^2 - 6x + 9 = x+1 -2(x-2)

x^2 - 6x + 9 = -x -1

x^2 -5x + 10 = 0

x = [5 +/- sqrt(25 - 40)]/2

sqrt(x+4)-2sqrt(x-1) = -1

Square everything:

(x+4) + 4(x-1) - 4sqrt(x^2+3x-4) = -1

x+4 + 4x - 1 - 4qrt(x^2+3x-4) = -1

5x + 4 = sqrt(x^2+3x-4)

Square again:

25x^2 + 40x + 16 = x^2 + 3x - 4

24x^2 + 37x + 20 = 0

x = [-37 +/- sqrt(37^2-4*24*20)]/(48)

sqrt(x)-sqrt(x-1) = 1

Square everything:

x + x-1 - 2*sqrt(x^2-x) = 1

2x - 2 = 2 sqrt(x^2-x)

Square again:

4x^2 - 8x + 4 = 2*x^2-2*x

2x^2 - 6x + 4 = 0

x^2 - 3x + 2 = 0

(x-1)(x-2) = 0

x = 1, 2

1+sqrt(x+7) = sqrt(2x+7)

Square each, again~!

1 + x+7 + 2sqrt(x+7) = 2x+7

2sqrt(x+7) = x-1

Square again:

4 * (x + 7) = x^2 - 2x + 1

4x + 28 = x^2-2x+1

x^2 - 6x - 27 = 0

(x-9)(x-3) = 0

x = 9, 3

it fairly is complicated to tell from the way you have written it precisely what's decrease than the novel. it may help to apply ( )'s. although, the customary rule for fixing equations with radicals, is to isolate the novel on one edge and then sq. the two aspects. you could ought to try this extra desirable than as quickly as. Then, continuously verify the solutions, with the aid of fact squaring the two aspects introduces extraneous roots. occasion: ?(x+3) - ?(x-2) = a million isolate one radical: ?(x+3) = a million + ?(x-2) sq. the two aspects: x+3 = a million + 2?(x-2) + x-2 simplify and isolate the the rest radical: 2?(x-2) = 4 ?(x-2) = 2 sq. the two aspects: x - 2 = 4 answer: x = 6 verify: ?(6+3) - ?(6-2) = a million ?9 - ?4 = a million 3 - 4 = a million NO, would not verify there's no answer to this issue. it fairly is it! ;)