Question

In the following, determine whether the given number are the solution of the given equation or not:

`x^2 - sqrt2 x -4=0; x= -sqrt2`

Answer 1

Given:

`x^2 - sqrt2 x -4=0; x= -sqrt2`

Verification

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

`x^2 - sqrt2 x -4`

`= (-sqrt2)^2 - sqrt2 (-sqrt2)-4`

= 2 + 2 − 4

= 0

LHS = 0 = RHS,

`x= -sqrt2`​ is a solution of `x^2−sqrt2​x−4=0​`