Question

Solve the following quadratic equation by formula method

`sqrt(2)"f"^2 - 6"f" + 3sqrt(2)` = 0

Answer 1

Here a = `sqrt(2)`, b = – 6 and c = `3sqrt(2)`

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

= `(6 ± sqrt(36 - 4(sqrt(2))(3sqrt(2))))/(2sqrt(2))`

= `(6 ± sqrt(36 - 24))/(2sqrt(2))`

= `(6 ± sqrt(12))/(2sqrt(2))`

= `(6 ±2sqrt(3))/(2sqrt(2))`

= `(2[3 ±sqrt(3)])/(2sqrt(2))`

= `(3 ± sqrt(3))/sqrt(2)`

The solution set is `(3 + sqrt(3))/sqrt(2)` and `(3 - sqrt(3))/sqrt(2)`