ANSWERS:

1.x4-13x+36=0
  (x²-9)(x²-4)
  Let x²=k
  k=9   k=4
  x²=9   x²=4
  x=+3 -3   x=+2 -2

2. 1     2 
  ___ - ___ - 3=0
   x²    x

( 1      ) ( 1 + 1)
 ___ - 3    ___ 
  x          x

Let 1
   ___ = k
    x

(k-3) (k+1)
 k=3   k=-1

 1        1
___ = 3  ___ =-1
 x        x 


   1      1
x=___ x=-___
   3      1
      x=-1

3.6y-2+y-1-2=0
  (3y-1+2) (2y-1-1)
  y-1= - 2    y-1= 1
       ___         ___
        3           2

  y= -3                   y=2   
     ___
      2 
4. (x²-3x)²-20=8(x²-3x)
   Let (x²-3x)=k
   k²-20=8k
   k²-8k-20
   (k-10)(k+2)
   k=10 k=-2

   x²-3x=10          x²-3x=-2
   x²-3x-10          x²-3x+2
   (x+5)(x-2)        (x-2)(x-1)
    x=5  x=-2         x=2  x=1

5. (x²+3x)²-2(x²+3x)-8=0
    x²+3x=k
    k²-2k-8=0
    (k-4)(k+2)
     k=4  k=-2
     x²+3x=4       x²+3x=-2 
     x²+3x-4       x²+3x+2
     (x+4)(x-1)    (x+2)(x+1)
      x=-4 x=1      x=-2 x=-1

6. y²-y-3=   9
           _____
            y²-y-3

  k=y²-y-3

  k=  9
    _____
      k

  k=--3 +3
   
  y²-y-3=3                y²-y-3=-3
  y²-y-6                  y²-y-3+3
  (y-3)(y+2)              y(y-1)
   y=3  y=-2              y=0 y=1

7.(x²-2x)²-2(x²-2x)-3=0
   Let k=x²-2x
     k²-2k-3=0
     (k-3)(k+1)
      k=3  k=-1
   x²-2x=3            x²-2x=-1
   x²-2x-3            x²-2x+1
   (x-3)(x+1)         (x-1)(x-1)
    x=3  x=-1          x=1

8. (x²-5x)²=36
      k²=36
      k= +6  -6
    x²-5x=6           x²-5x=-6
    x²-5x-6           x²-5x+6
    (x-6)(x+1)        (x-3)(x-2)
     x=6 x=-1          x=3  x=2

9. (2x²+5x)²-10x²-25x-14=0
   (2x²+5x)²-5(2x²+5x)=14
   Let 2x²+5x=k
       k²-5k=14
       k²-5k-14
       (k-7)(k+2)
        k=7  k=-2
 2x²+5x=7          2x²+5x=-2
 2x²+5x-7          2x²+5x+2
(2x+7)(x-1)        (2x+1)(x+2)
      7                 1
 x= -__   x=1      x= -___  x=-2 
     2                  2

10. x²-5x+2-   4        
             _______   =0
             x²-5x+2
   k- 4   
     ___     =0
      k

   k²-4=0
   (k-2)(k+2)
    k=2  k=-2
    x²-5x+2=2            x²-5x+2=-2
    x(x-5)               (x-4)(x-1)
    x=0 x=5               x=4 x=1