Question

Which of the following equation is an identity?

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

Answer 1

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

If 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.
$a.(x-2{)}^2=x^2-4x+4\Rightarrow x^2-4x+4=x^2-4x+4\Rightarrow x^2\times 0-x\times 0+4\times 0=0$
Which is true for all values of $x.$
Thus, this equation is an identity.

$b.x^2-4x+4=0\Rightarrow (x-2{)}^2=0\Rightarrow x=2$
This means the equation is satisfied for $x=2$
Thus, this equation is not an identity.

$c.(x+3{)}^2=x^2+5x+8\Rightarrow x^2+6x+9=x^2+5x+8\Rightarrow x=-1$
This means the equation is satisfied for $x=-1$
Thus, this equation is not an identity.

$d.2x-1=0\Rightarrow x=0.5$
This means the equation is satisfied for $x=0.5$
Thus, this equation is not an identity.