Question

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

`2x^2 - 2sqrt6x + 3 =0; x = sqrt3`

Answer 1

Given:

`2x^2 - 2sqrt6x + 3 =0`

Verification

Substitute `x = sqrt3​` in the left-hand side (LHS):

`2(sqrt3)^2-2sqrt6(sqrt3)+3`

`=2(3)-2sqrt18+3`

`= 6-2(3sqrt2)+3`

`=6-6sqrt2+3`

`=9-6sqrt2`

LHS = 9 − `6sqrt2 \cancel=0`,

`x = sqrt3` is not a solution of `2x^2 - 2sqrt6x + 3 =0`