Question

Which of the following equation is an identity?

• A. $x^2-4x+4=0$
• B. ${(x-2)}^2=x^2-4x+4$
• C. ${(x+3)}^2=x^2+5x+8$
• D. $2x-1=0$

Answer 1

The correct option is B ${(x-2)}^2=x^2-4x+4$

Solution: If a statement is true for all the values of the variable, such statements are called identities.

(a) → is true for all values of $x$

(b) → is true only for $x=2$

(c) → is true only for $x=-1$

(d) → is true only for $x=\frac{1}{2}$

Hence, (a) is an identity.