Find a quadratic equation whose product of roots `x_1 a n d x_2` is equal to 4 and satisfying the relation `(x_1)/(x_1-1)+(x_2)/(x_2-1)=2.`

Explanation

Since `x_(1) x_(2) = 4`
or `x_(2) = (4)/(x_(1))`
`therefore (x_(1))/(x_(1)-1) + (x_(2))/(x_(2)-1) = 2`
or `(x_(1))/(x_(1)-1) + ((4)/(x_(1)))/((4)/(x_(1))-1) = 2`
or `(x_(1))/(x_(1)-1) + (4)/(4-x_(1)) =2`
or `4x_(1) -x_(1)^(2) + 4x_(1)-4 =2(x_(1) -1) (4-x_(1))`
or `x_(1)^(2) -2x_(1)+4=0`
or `x^(2)-2x+ 4 =0`, Which is required equation.