Question

In the following, show that the given numbers are the solution of the given equation:

`x^2 + 3sqrt2x - 8=0; x = sqrt2`

Answer 1

Given:

`x^2 + 3sqrt2x - 8=0`

Verification

Substitute `x = sqrt2` in the left-hand side (LHS):

`x^2 + 3sqrt2x - 8`

`= (sqrt2)^2 + 3sqrt2 (sqrt2) - 8`

= 2 + 3(2) − 8

= 2 + 6 − 8

= 0

Since LHS = 0, which equals the RHS,

`x = sqrt2`is a solution of `x^2 + 3sqrt2x - 8=0`