SOLUTION: How do i make an appropriate substitution?(y-10/y)^2 -6(y-10/y)-27=0

Question 117397: How do i make an appropriate substitution?(y-10/y)^2 -6(y-10/y)-27=0
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
(y-10/y)^2 -6(y-10/y)-27=0
Let (y-10/y)=x
x^2-6x-27=0
(x-9)(x+3)=0
.
y-10/y-9=0 substitute (y-10/y) back in for x.
y^2-10-9y=0 Multiply each side times y to eliminate fraction.
y^2-9y-10=0
(y-10)(y+1)=0
.
y-10/y+3=0
y^2-10+3y=0
y^2+3y-10=0
(y+5)(y-2)=0
.
y=10, y=-1, y=-5, y=2
.
you can also solve this by graphing.
.
Ed

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