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

$$Giventhat(a+b)=\sqrt{3\sqrt{3}-\sqrt{2}}$$$$and(a-b)=\sqrt{3\sqrt{2}-\sqrt{3}}$$$$Find$$$$\left(i\right)ab\left(ii\right)a^2+b^2$$

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

$${(\mathrm{a}-\mathrm{b})}^2={\mathrm{a}}^2+{\mathrm{b}}^2-2\mathrm{ab}$$$$={(\mathrm{a}+\mathrm{b})}^2-4\mathrm{ab}$$$$\Rightarrow 4\mathrm{ab}={(\mathrm{a}+\mathrm{b})}^2-{(\mathrm{a}-\mathrm{b})}^2$$$$=4(\sqrt{3}-\sqrt{2})\Rightarrow \mathrm{ab}=\sqrt{3}-\sqrt{2}$$$$\Rightarrow {\mathrm{a}}^2+{\mathrm{b}}^2={(\mathrm{a}+\mathrm{b})}^2-2\mathrm{ab}=\sqrt{3}+\sqrt{2}$$

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