Question

Solve the following equation using the formula: 

`x^2 - 6 = 2sqrt(2)x` 

Answer 1

`x^2 - 6 = 2sqrt(2)x` 

`\implies x^2-2sqrt2x-6=0` 

Here a = 1, b = `-2sqrt(2)` and c = − 6 

Then `x = (-b +- sqrt(b^2 - 4ac))/(2a)`  

= `(-(-2sqrt2) +- sqrt((-2sqrt(2))^2 - 4(1)(-6)))/(2(1))`  

= `(2sqrt(2) +- sqrt(32))/2`

= `(2sqrt(2) +- 4sqrt(2))/2`

= `(2sqrt(2) + 4sqrt(2))/2` and `(2sqrt(2) - 4sqrt(2))/2` 

= `(6sqrt(2))/2` and `(-2sqrt(2))/2`

= `3sqrt(2)` and `-sqrt(2)`