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Question

# Which of the following equation is an identity?

A
2x1=0
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B
(x2)2=x24x+4
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C
x24x+4=0
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D
(x+3)2=x2+5x+8
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Solution

## The correct option is B (x−2)2=x2−4x+4If a statement is true for all the values of the variable, such statements are called identities. Now, let's look at equations one by one. a.(x−2)2=x2−4x+4⇒x2−4x+4=x2−4x+4⇒x2×0−x×0+4×0=0 Which is true for all values of x. Thus, this equation is an identity. b.x2−4x+4=0⇒(x−2)2=0⇒x=2 This means the equation is satisfied for x=2 Thus, this equation is not an identity. c.(x+3)2=x2+5x+8⇒x2+6x+9=x2+5x+8⇒x=−1 This means the equation is satisfied for x=−1 Thus, this equation is not an identity. d.2x−1=0⇒x=0.5 This means the equation is satisfied for x=0.5 Thus, this equation is not an identity.

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