Question

(x^2-2x)^2-23(x^2-2x)+120=0

Answer 1

Step-by-step explanation:

let x²-2x=a

then, a²-23a+120=0

a²-15a-8a+120=0

a(a-15)-8(a-15)=0

(a-8)(a-15)=0

so, a=8 or a=15

then, x²-2x=8 or, x²-2x=15

x²-2x-8=0 or, x²-2x-15=0

by solving, we get

x=4, or x=(-2). and x=5 or (-3)

but here signs change two times then

all the roots are positive

hence, x=4 and 5