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2016-04-19T20:23:15+05:30
(x_1-x_2)^2=x_1^2-2x_1x_2+x_2^2\\(x_1+x_2)^2=x_1^2+2x_1x_2+x_2^2=x_1^2+2x_1x_2-4x_1x_2+x_2^2+4x_1x_2=\\x_1^2-2x_1x_2+x_2^2+4x_1x_2=(x_1-x_2)^2+4x_1x_2\\(x_1-x_2)^2=(x_1+x_2)^2-4x_1x_2

On the basis of Viete formulas for zeroes of polynomial:
f(x)=ax^2+bx+c\\x_1+x_2=\frac{-b}a\\x_1\times{x}_2=\frac{c}a\\(x_1-x_2)^2=(\frac{-b}a)^2-4\times\frac{c}a=(\frac{-p}1)^2-4\times\frac{45}1=144\\p^2=144+180\\p^2=324\\|p|=\sqrt{324}\\p=18\ or\ p=-18\\f(x)=x^2+18x+45\ or\ f(x)=x^2-18x+45\\x_1=3\ or\ x_1=-15\\x_2=15\ or\ x_2=-3\\(3-15)^2=144\ or\ (-15-(-3))^2=144
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