Solve the following quadratic equations by completing the square method.
`9y^(2)-12y+2=0`

Answer

`(2-sqrt2)/(3),(2+sqrt2)/(3)` are the roots of the given quadratic equation.

Explanation

`9y^(2)-12y+2=0`
`:.y^(2)-(12y)/(9)+(2)/(9)=0" "` (Dividing by 9 )
`:.y^(2)-(4y)/(3)+(2)/(9)=0`
Comparing `y^(2)-(4y)/(3)"with "y^(2)-2yz`
`-2yz=-(4y)/(3):.z=(2)/(3).:.z^(2)=(4)/(9)`
`:.y^(2)-(4y)/(3)+(2)/(9)=0` is a perfect square trinomial.
`y^(2)-(4y)/(3)+(2)/(9)=0`
`:.y^(2)-(4y)/(3)+(4)/(9)-(4)/(9)+(2)/(9)=0`
`:.(y-(2)/(3))^(2)-((4)/(9)-(2)/(9))=0`
`:.(y-(2)/(3))^(2)-((2)/(9))=0`
`:.(y-(2)/(3))^(2)-((sqrt3)/(3))^(2)=0`
`:.(y-(2)/(3)+(sqrt3)/(3))(y-(2)/(3)-(sqrt2)/(3))=0`
`:.y-(2)/(3)+(sqrt(2))/(3)=0ory-(2)/(3)+(sqrt2)/(3)=0`
`:.y=(2-sqrt2)/(3)ory=(2+sqrt2)/(3)`