Show that A = B where A = {x│x² - 4x +4 =1}, B = {1,3}

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Solution:

A = {x│x² - 4x +4 =1}

$x^2-4x+4=1 \\\Rightarrow x^2-4x+3=0 \\\Rightarrow x^2-3x-x+3=0 \\\Rightarrow (x-3)(x-1)=0 \\\Rightarrow x-3=0, x-1=0 \\\Rightarrow x=3, x=1$

Thus, A = {3,1}

And B = {1,3} is given

So, A = B

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