Question

Solve the following quadratic equation by formula method

36y² – 12ay + (a² – b²) = 0

Answer 1

Here a = 36, b = – 12a, c = a² – b² 

x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`

= `(12"a" ± sqrt(144"a"^2 - 4(36)("a"^2 - "b"^2)))/(2(36))`

= `(12"a" ± sqrt(144"a"^2 - 144"a"^2 + 144"b"^2))/(72)`

= `(12"a" ± sqrt(144"b"^2))/(72)`

= `(12"a" ± 12"b")/(72)`

= `(12("a" ± "b"))/(72)`

= `(("a" ± "b"))/(6)`

= `(("a" + "b""))/(6)` or `(("a" - "b"))/(6)`

The solution set is `(("a" + "b""))/(6)` and `(("a" - "b"))/(6)`