F.4 MATHS!

1) x + 1/x = 5/2
2x^2 + 2 = 5x
2x^2 - 5x + 2 = 0
(x-2) (2x-1) = 0
x = 2 or x = 1/2

5) 6/x - 2/x-1 = 1
6(x-1) - 2x = x(x-1)
6x - 6 - 2x = x^2 - x
x^2 - 5x + 6 = 0
(x - 2) (x - 3) = 0
x = 2 or x = 3

17) x^4 - 7x^2 - 18 = 0
(x^2 + 2) (x^2 - 9) = 0
x^2 = 9
x = +3 or -3

19) 2x^4 - 7x^2 - 4 = 0
(x^2 - 4) (2x^2 + 1) = 0
x^2 = 4
x = +2 or -2

22) (x+1)^4 - 10(x+1)^2 + 9 = 0
[(x+1)^2 - 9] [(x+1)^2 -1] = 0
(x+1) = 3 or (x+1) = -3 or (x+1) = 1 or (x+1) = -1
x = 2 or x = -4 or x = 0 or x = -2

1)
X + (1/X) = 5/2
(X^2+1)/X = 5/2
2X^2-5X+2 = (2X-1)(X-2), X=1/2 or 2

5)
(6/X)-2/(X-1)=1
[6(X-1)-2X]/[X(X-1)]=1
6X-6-2X = X^2-X
X^2-5X+6 = (X-3)(X-2), X=3 or 2

17)
X^4-7X^2-18=0
(X^2)^2-7(X^2)-18=0-(X^2-9)(X^2+2), X^2=9 or 2 then X=+-3 or square root (2) * j
where j=square root(-1)

19)
2X^4-7X^2-4=0
2(X^2)^2-7(X^2)-4=0=(2X^2+1)(X^2-4), X^2=-1 or 4 then X=j or +-2
where J = square root(-1)

22)
(X+1)^4-10(X+1)^2+9=0
[(X+1)^2]^2-10[(X+1)^2]+9=0=[(X+1)^2-1][(X+1)^2-9], (X+1)=+-1 or +-3 then
X=-2, 0, 2 or 4

1)
x + 1/x = 5/2
x^2 + 1 = 5/2x
x^2 - 5/2x + 1 = 0
(x - 2)(x - 1/2) = 0
x = 2 or x = 1/2

5)
6/x - 2/(x-1) = 1
6(x-1) - 2x = x(x-1)
6x - 6 - 2x = x^2 - x
x^2 - 5x + 6 = 0
(x-2)(x-3) = 0
x = 2 or x = 3

17)
x^4 - 7x^2 - 18 = 0
(x^2 - 9)(x^2 + 2) = 0
x^2 = 9 or x^2 = -2 (rejected)
x = 3 or x = -3

19)
2x^4 - 7x^2 - 4 = 0
(2x^2 + 1)(x^2 - 4) = 0
x^2 = -1/2 (rejected) or x^2 = 4
x = 2 or x = -2

22)
(x+1)^4 - 10(x+1)^2 + 9 = 0
[(x+1)^2 - 9][(x+1)^2 - 1] = 0
(x+1)^2 = 9 or (x+1)^2 = 1
(x+1) = 3 or (x+1) = -3 or (x+1) = 1 or (x+1) = -1
x = 2 or x = -4 or x = 0 or x = -2