Given-that-a-b-3-3-2-and-a-b-3-2-3-Find-i-ab-ii-a-2-b-2-

Question Number 146325 by 7770 last updated on 12/Jul/21

G i v e n t h a t (a + b) = \sqrt{3 \sqrt{3} - \sqrt{2}}

a n d (a - b) = \sqrt{3 \sqrt{2} - \sqrt{3}}

F i n d

(i) a b (i i) a^{2} + b^{2}

Answered by Ar Brandon last updated on 12/Jul/21

{(a - b)}^{2} = a^{2} + b^{2} - 2 ab

= {(a + b)}^{2} - 4 ab

\Rightarrow 4 ab = {(a + b)}^{2} - {(a - b)}^{2}

= 4 (\sqrt{3} - \sqrt{2}) \Rightarrow ab = \sqrt{3} - \sqrt{2}

\Rightarrow a^{2} + b^{2} = {(a + b)}^{2} - 2 ab = \sqrt{3} + \sqrt{2}