if-a-b-R-and-a-2-1-b-2-1-9-6-a-b-find-a-2-b-2-

Question Number 151391 by mathdanisur last updated on 20/Aug/21

if a; b \in R and

(a^{2} + 1) (b^{2} + 1) + 9 = 6 (a + b)

find a^{2} + b^{2} = ?

Answered by dumitrel last updated on 20/Aug/21

(a^{2} + 1) (b^{2} + 1) \overset{c b s}{⩾} {(a + b)}^{2} \Rightarrow

6 (a + b) ⩾ {(a + b)}^{2} + 9 \Rightarrow {(a + b - 3)}^{2} ⩽ 0

a + b = 3 \Rightarrow {(a b)}^{2} + 9 - 2 a b + 1 = 9 \Rightarrow a b = 1 \Rightarrow

a^{2} + b^{2} = 7

Commented by mathdanisur last updated on 20/Aug/21

Thank You S er Cool