Determine whether the given values are solutions of the given equation

1.	Determine whether the given values are solutions of the given equation or not:x2 − 3√3x + 6 = 0 , x = √3 and x = −2√3
Answer» Here we have, LHS = x²− 3√3x + 6 Substituting x = √3 in LHS, we get (√3)²− 3√3(√3) + 6 ⇒ 3 – 9 + 6 = 0 = RHS ⇒ LHS = RHS Thus, x = √3 is a solution of the given equation. Similarly, Substituting x = −2√3 in LHS, we get (-2√3)²− 3√3(-2√3) + 6 ⇒ 12 + 18 + 6 = 36 ≠ RHS ⇒ LHS ≠ RHS Thus, x = −2√3 is not a solution of the given equation.

Determine whether the given values are solutions of the given equation or not:x2 − 3√3x + 6 = 0 , x = √3 and x = −2√3

Answer»

Here we have,

LHS = x²− 3√3x + 6

Substituting x = √3 in LHS, we get

(√3)²− 3√3(√3) + 6

⇒ 3 – 9 + 6 = 0 = RHS

⇒ LHS = RHS

Thus, x = √3 is a solution of the given equation.

Similarly,

Substituting x = −2√3 in LHS, we get

(-2√3)²− 3√3(-2√3) + 6

⇒ 12 + 18 + 6 = 36 ≠ RHS

⇒ LHS ≠ RHS

Thus, x = −2√3 is not a solution of the given equation.