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Question
Solve the following quadratic equation by formula method
36y2 – 12ay + (a2 – b2) = 0
Solution
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)`
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