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question about 3.23

 
 
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Re: question about 3.23
by Areteem Professor - Tuesday, June 23, 2020, 9:48 PM
 

Using Vieta's formulas, we see that $$x_1^2 + x_2^2 = (x_1 + x_2)^2 -2x_1 x_2 = (-a)^2 -2(b) = a^2 -2b.$$The problem tells us that we also have $x_1^2 + x_2^2 = 1$, so $a^2 -2b = 1$, that is, $1 + 2b = a^2$. Regardless of the value of $a$, we have that $a^2 \geq 0$, so $1 + 2b \geq 0$.