Question

Solve
2(x+1/x)²-7(x+1/x)+6=0

Answer 1

let us take x+1/x=t
Then the equation becomes
2t²-7t+6=0
Byfactorization
2t²-4t-3t+6=0
Taking 2t as common in first two terms and -3 as common in next two terms
2t(t-2)-3(t-2)=0
Take t-2 as common
(2t-3)(t-2)=0
By using the principle of zer product
2t-3=0      or      t-2=0
2t=3         or         t=2
  t=3/2       or         t=2
x+1/x=2
x²+1/x=2
Multiplying both sides by x
x²+1=2x
Adding -2x on both sides
x²-2x+1=0
BY factorization
x²-x-x+1=0
Taking x as common in first two terms and -1 as common in next two terms
x(x-1)-1(x-1)=0
Take (x-1) as common
(x-1)²=0
x-1=0
x=1