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Question

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If ${y^2} - 3 = 0,$ then $y = \pm \sqrt {3.} $

A. True

B. False

Answer
Verified

Hint: In order to comment about this question whether it is true or false, we will first factorize the given equation with the help of formula given as ${a^2} - {b^2} = (a + b)(a - b)$ then we get the solution.

Complete step-by-step answer:

Given equation is ${y^2} - 3 = 0$

We will factorize given equation to get the roots

$\left[ {\because {a^2} - {b^2} = (a + b)(a - b)} \right]$

Here $a = y{\text{ and }}b = \sqrt 3 $

By substituting the values in above formula, we get

\[

\Rightarrow {y^2} - {\left( {\sqrt 3 } \right)^2} = 0 \\

\Rightarrow (y + \sqrt 3 )(y - \sqrt 3 ) = 0 \\

\Rightarrow y = - \sqrt 3 {\text{ or }}\sqrt 3 \\

\Rightarrow y = \pm \sqrt 3 \\

\]

Hence, the solution of ${y^2} - 3 = 0$ is \[y = \pm \sqrt 3 \]. Therefore the given statement is true.

Note: In order to solve these types of questions, remember all the algebraic identities. These questions are based on simple arithmetic operations and few identities. By convention, letters at the beginning of the alphabet (e.g. a, b, c) are typically used to represent constants, and those toward the end of the alphabet (e.g. x, y, z ) are used to represent variables. They are usually written in italics.

Complete step-by-step answer:

Given equation is ${y^2} - 3 = 0$

We will factorize given equation to get the roots

$\left[ {\because {a^2} - {b^2} = (a + b)(a - b)} \right]$

Here $a = y{\text{ and }}b = \sqrt 3 $

By substituting the values in above formula, we get

\[

\Rightarrow {y^2} - {\left( {\sqrt 3 } \right)^2} = 0 \\

\Rightarrow (y + \sqrt 3 )(y - \sqrt 3 ) = 0 \\

\Rightarrow y = - \sqrt 3 {\text{ or }}\sqrt 3 \\

\Rightarrow y = \pm \sqrt 3 \\

\]

Hence, the solution of ${y^2} - 3 = 0$ is \[y = \pm \sqrt 3 \]. Therefore the given statement is true.

Note: In order to solve these types of questions, remember all the algebraic identities. These questions are based on simple arithmetic operations and few identities. By convention, letters at the beginning of the alphabet (e.g. a, b, c) are typically used to represent constants, and those toward the end of the alphabet (e.g. x, y, z ) are used to represent variables. They are usually written in italics.

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