Question

9(x^2+1/x^2) - 9(x+1/x) - 52 = 0​

Answer 1

Step-by-step explanation:

x+1/x=y

squaring on both sides

x²+1/x²+2=y²

x²+1/x²=y²-2

9(y²-2)-9(y)-52=0

9y²-18-9y-52=0

9y²-9y-70=0

9y²-30y+21y-70=0

3y(3y-10)+7(3y-10)=0

(3y+7)(3y-10)=0

3y+7=0. 3y-10=0

3y=-7. 3y=10

y=-7/3. y=10/3