Question

In each of the following, determine whether the given values are solution of the given equation or not:
`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`

Answer 1

`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`
Now x = `-sqrt(2)`
⇒ L.H.S. = `(-sqrt(2))^2 - sqrt(2) xx (-sqrt(2)) - 4 = 0`
= 2 + 2 - 4
= 0
= R.H.S.
∴ x = `-sqrt(2)` is a solution of the given equation.
Now x = `-2sqrt(2)`
⇒  L.H.S. = `(-2sqrt(2))^2 - sqrt(2)(-2sqrt(2)) - 4 = 0`
= 8 + 4 - 4 ≠ 0 ≠ R.H.S.
∴ x = `-2sqrt(2)`  is not a solution of the equation.