F.4 equations!!

1.) x - 4 = √( x + 2)
(x – 4)^2 = x + 2
x^2 – 8x + 16 – x – 2 = 0
x^2 – 9x + 14 = 0
(x -2)(x – 7) = 0
x = 7

2.) 4^ x(x+1) - 8^ x+2 = 0
2^ 2x(x+1) - 2^ 3x+6 = 0
2^ 2x(x+1) = 2^ 3x+6
2x(x+1) = 3x+6
2x^2 + 2x = 3x + 6
2x^2 –x – 6 + 0
(2x + 3) (x – 2) = 0
x = -1.5 or x = 2

3.) √(X-2) +1 = 6/√(X-2)
Let k = (x – 2)^0.5
k + 1 = 6/k
k(k +1) = 6
k^2 + k – 6 = 0
(k + 3)(k – 2)
k = 2 or k = -3
(x-2)^0.5 = -3 (drop this one)
(x-2)^0.5 = 2
x – 2 = 2^2
x = 6

4.) Please check to see if you miss a term, + 6

2X ^2 + X + (+ 6) + √(2X^ 2 +X +6) - 12 =0

2011-05-04 08:39:03 補充：
4)
2x^2 + x + √(2x^2 + x - 6 ) -12 = 0
2x^2 + x – 6 + √(2x^2 + x - 6 ) -12 +6 = 0
Let w = √(2x^2 + x - 6 )
w^2 + w – 6 = 0
(w + 3) (w -3) = 0
3 = √(2x^2 + x - 6 )
9 = 2x^2 + x - 6
2x^2 + x –15 = 0
(2x – 5)(x + 3) = 0
x = -3 or x = 2.5

Note: √9 can be +3 or -3 when checking

2011-05-04 08:56:08 補充：
Solution to Ques. 4 and checking are also sent to your Email.