Solve for sqrt(x^2 - 4x +4) =0

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

sqrt(x^2 - 4x + 4) = 0

Let us rewrite:

x^2 - 4x + 4 = (x-2)^2

==> sqrt(x-2)^2 = 0

==> x-2 = 0

==> x =2

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

We know:

(a + b)^2 = a^2 - 2ab + b^2

Making a = x and b = 2, the above formula becomes:

(x - 2)^2 = x^2 - 2*x*2 +2^2

= x^2 - 4x + 4

Therefore:

sqrt(x^2 - 4x + 4) = sqrt[(x - 2)^2]

= x - 2

Substituting this value of sqrt(x^2 - 4x + 4) in given equation:

x - 2 = 0

==> x = 2

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