a-b-gt-0-1-a-1-b-2-and-a-2-b-2-12-a-b-

Question Number 213621 by hardmath last updated on 10/Nov/24

a, b > 0

\frac{1}{a} + \frac{1}{b} = 2 and a^{2} + b^{2} = 12

a + b = ?

Answered by Ghisom last updated on 10/Nov/24

\frac{1}{a} + \frac{1}{b} = 2 \Rightarrow 2 a b = a + b

a^{2} + 2 a b + b^{2} = 12 + 2 a b

{(a + b)}^{2} = 12 + (a + b)

{(a + b)}^{2} - (a + b) - 12 = 0

a + b = \frac{1}{2} \pm \frac{7}{2}

a, b > 0 \Rightarrow a + b = 4

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