Question

Determine whether x = √3 and x = —2√3 are solutions of the equation x2 – 3√3x + 6 = 0

Answer 1

Question:

Determine whether x=√3 and x= -2√3 are the solutions of the equation x² - 3√3x + 6 = 0 or not.

Answer:

x = √3 is a solution but x = -2√3 is not a solutions of the given equation.

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

Solution:

The given equation is : x² - 3√3x + 6 = 0 ------(1)

Let's check whether x = √3 is a solution of eq-(1) or not .

Putting x = √3 in eq-(1) , we have ;

=> (√3)² - 3√3•√3 + 6 = 0

=> 3 - 9 + 6 = 0

=> 0 = 0 (which is true)

Since , eq-(1) is satisfied by x = √3 , thus x = √3 is a solution of eq-(1) .

Now,

Let's check whether x = -2√3 is a solution of eq-(1) or not .

Putting x = -2√3 in eq-(1) , we have ;

=> (-2√3)² - 3√3•(-2√3) + 6 = 0

=> 12 + 18 + 6 = 0

=> 36 = 0 (which is not true)

Since , eq-(1) is not satisfied by x = -2√3 ,

Thus x = -2√3 is not a solution of eq-(1).

Answer 2

$\huge{\boxed{\red{Answer}}}$

$\large{\underline{\pink{Required\;to\;find}}}$$Whether\;\sqrt{3}\;and\;-2\sqrt{3}\;are\;roots\;of\;equation\\ x^{2}-3\sqrt{3}x+6=0$

$\large{\underline{\pink{Verifying\;\sqrt{3}\;as\;a\;root}}}$

• Substituting $\sqrt{3}$ in the equation
• $x^{2}-3\sqrt{3}x+6=0$
• ${(\sqrt{3})}^{2}-3\sqrt{3}(\sqrt{3})+6=0$
• $3-9+6=0$
• 0=0

$\boxed{\green{Therefore\;\sqrt{3}\;is\;a\;root}}$

$\large{\underline{\pink{Verifying\;-2\sqrt{3}\;as\;a\;root}}}$

• Substituting $-2\sqrt{3}$ in the equation
• $x^{2}-3\sqrt{3}x+6=0$
• ${(-2\sqrt{3})}^{2}-3\sqrt{3}(-2\sqrt{3})+6=0$
• 12+18+6=0
• 36=0

False statement

$\boxed{\green{Therefore\;-2\sqrt{3}\;is'nt\;a\;root}}$

$\boxed{\red{Therefore\;\sqrt{3}\;is\;a\;root\;and\;-2\sqrt{3}\;is'nt\;a\;root\;of\;given\;equation}}$

$\huge{\boxed{\blue{NOTE}}}$

• If 'a' is aroot of a given equation then it must satisfy the given equation
• I have used the above statement to verify -3 as root of given equation