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Suppose r and s are the solutions of x^2 − 12x + 22 = 0. Find r^2 + s^2 .

 

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 Jun 12, 2023
 #1
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By the quadratic formula, the roots of x^2 - 12x + 22 = 0 are 6 + sqrt(18) and 6 - sqrt(18).

 

Then r^2 + s^2 = (6 + sqrt(18))^2 + (6 - sqrt(18))^2

= 36 + 12 sqrt(18) + 18 + 36 - 12 sqrt(18) + 18

= 108

 Jun 12, 2023
 #2
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actually its 100 according to Vieta's formulas

Guest Jun 12, 2023

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