Question

Determine whether (i) x= √2, (ii) x = –2√2 are the solutions of the equation x2 + √2 x – 4 = 0 or not.

Answer 1

Question:

Determine whether x=√2 and x=-2√2 are the solutions of the equation x² + √2x - 4 = 0 or not.

Answer:

x = √2 and x = -2√2 are the 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 + √2x - 4 = 0 ------(1)

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

Putting x = √2 in eq-(1) , we have ;

=> (√2)² + √2•√2 - 4 = 0

=> 2 + 2 - 4 = 0

=> 0 = 0 (which is true)

Since , eq-(1) is satisfied by x = √2 , thus x = √2 is a solution of eq-(1) .

Now,

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

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

=> (-2√2)² + √2•(-2√2) - 4 = 0

=> 8 - 4 - 4 = 0

=> 0 = 0 (which is true)

Since , eq-(1) is satisfied by x = -2√2 ,

Thus x = -2√2 is a solution of eq-(1).

Answer 2

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

$\large{\underline{\pink{Required\;to\;find}}}$

$Whether\;\sqrt{2}\;and\;-2\sqrt{2}\;are\;roots\;of\;equation\\ x^{2}+\sqrt{2}x-4=0$

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

• Substituting $\sqrt{3}$ in the equation
• $x^{2}+\sqrt{2}x+6=0$
• ${(\sqrt{2})}^{2}+\sqrt{2}(\sqrt{2})-4=0$
• $2+2-4=0$
• 0=0

$\boxed{\green{Therefore\;\sqrt{2}\;is\;a\;root}}$

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

• Substituting $-2\sqrt{2}$ in the equation
• $x^{2}+\sqrt{2}x-4=0$
• ${(-2\sqrt{2})}^{2}+\sqrt{2}(-2\sqrt{2})-4=0$
• 8-4-4=0
• 0=0

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

$\boxed{\red{Therefore\;\sqrt{2}\;and\;-2\sqrt{2}\;are\;roots\;of\;given\;equation}}$

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

• If 'a' is a root 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