Question

6x^-2 -7x^-1 +1=0
Solve by making appropriate substitutions

Answer 1

Let
`y=x^(-1)`, so that
`y^2=x^(-2)`. Then


`6x^(-2)-7x^(-1)+1=0\iff6y^2-7y+1=0\implies (6y-1)(y-1)=0`

which has two solutions,
`y=\frac16` and
`y=1`. So the solutions in terms of
`x` would be


`x^(-1)=\frac16\implies x=6`

`x^(-1)=1\implies x=1`