MATHS F.4......THX!!!

76.)
x=10-2√(x-2)
x - 2 - 8 = -2√(x-2)
(x-2) + 2√(x-2) - 8 = 0
[√(x-2)+4][√(x-2)-2] = 0
√(x-2) =-4(rej.) or √(x-2) = 2
x-2 = 4
x = 6
77.)
(x-2/x)^2 + (x-2/x) - 2 = 0
[(x-2/x)+2][(x-2/x)-1]=0
x-2/x +2 = 0 or x-2/x -1=0
x^2 + 2x - 2 = 0 or x^2 - x - 2 = 0
x = -1+/-√3 or (x-2)(x+1) = 0
x = -1+/-√3 or 2 or -1
78.)
(x^2 - 2x)^2 - 2x^2 + 4x - 3 = 0
(x^2 - 2x)^2 - 2(x^2 - 2x) - 3 = 0
[(x^2 - 2x) - 3][(x^2 - 2x)+1] = 0
x^2 - 2x - 3 = 0 or x^2 - 2x + 1 = 0
(x-3)(x+1) = 0 or (x-1)^2 = 0
x = 3 or -1 or 1
79.)
(x^2 -4x)^2 -8(x^2 - 4x) - 48 = 0
[(x^2 - 4x) - 12][(x^2 - 4x) + 4] = 0
x^2 - 4x - 12 = 0 or x^2 - 4x + 4 = 0
(x-6)(x+2) = 0 or (x-2)^2 = 0
x = 6 or -2 or 2
80.)
(x^2 + 2x) + 5(x^2 + 2x) + 4 = 0
[(x^2 + 2x) + 4][(x^2 + 2x) + 1] = 0
x^2 + 2x + 4 = 0 (rej.) or x^2 + 2x + 1 = 0
(x+1)^2=0
x = -1
97a.)
(x+1/x)^2 = 4
[(x+1/x) - 2][(x+1/x)+2] = 0
x+1/x - 2 = 0 or x + 1/x + 2 = 0
x^2 - 2x + 1 = 0 or x^2 + 2x + 1 = 0
(x-1)^2 = 0 or (x+1)^2 = 0
x = 1 or -1
b.)
1/(2x+1) * [1/(2x+1) + 3] = 10
[1/(2x+1)]^2 + 3[1/(2x+1)] - 10 = 0
[1/(2x+1) + 5][1/(2x+1) - 2] = 0
1/(2x+1) + 5 = 0 or 1/(2x+1) - 2 = 0
1 + 10x + 5 = 0 or 1 - 4x - 2 = 0
10x = -6 or 4x = -1
x = -3/5 or x = -1/4
99b.)
Let (x+2/x) be y,
(x+2/x)^2 - 4(x+2/x) +3 = 0
y^2 - 4y + 3 = 0
(y-3)(y-1) = 0
y = 3 or y = 1
x+2/x = 3 or x+2/x = 1
x^2 + 2 = 3x or x^2 + 2 = x
x^2 - 3x + 2 = 0 or x^2 - x + 2 = 0(rej.)
(x-2)(x-1) = 0
x = 2 or 1
100b.)
Let √(2x^2 + x - 6) be u,
2x^2 + x + √(2x^2 + x - 6) - 12 = 0
(2x^2 + x - 6) + √(2x^2 + x - 6) - 6 = 0
u^2 + u - 6 = 0
(u+3)(u-2)=0
u = -3 or 2
√(2x^2 + x - 6) = -3 (rej.) or √(2x^2 + x - 6) = 2
2x^2 + x - 6 = 4
2x^2 + x - 10 = 0
(2x+5)(x-2) = 0
x = -5/2 or 2