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Question Number 30148 by .none. last updated on 17/Feb/18

$$howtosolve\sqrt{{(c-\sqrt{-c})}^2}+\sqrt{{(c+6-\sqrt{-c})}^2}$$ $$2<a<3,-4<b<-3,c=\frac{a+b}{2}$$

Answered by mrW2 last updated on 17/Feb/18

$$-2<a+b<0$$ $$-1<c=\frac{a+b}{2}<0$$ $$letd=-c$$ $$0<d<1$$ $$\sqrt{{(c-\sqrt{-c})}^2}+\sqrt{{(c+6-\sqrt{-c})}^2}$$ $$=\sqrt{{(-d-\sqrt{d})}^2}+\sqrt{{(-d+6-\sqrt{d})}^2}$$ $$=\sqrt{{(d+\sqrt{d})}^2}+\sqrt{{(6-d-\sqrt{d})}^2}$$ $$=d+\sqrt{d}+6-d-\sqrt{d}$$ $$=6$$

Commented byMJS last updated on 17/Feb/18

$$\mathrm{you}\mathrm{had}\mathrm{been}\mathrm{slightly}\mathrm{faster}\mathrm{than}\mathrm{me};-)$$

Answered by MJS last updated on 17/Feb/18

$$\Rightarrow -1\leqq c<0$$ $$\Rightarrow \sqrt{{(c-\sqrt{-c})}^2}=\mid c-\sqrt{-c}\mid =\sqrt{-\mathrm{c}}-\mathrm{c}$$ $$\sqrt{{(c+6-\sqrt{-c})}^2}=\mid \mathrm{c}+6-\sqrt{-c}\mid =6-(\sqrt{-\mathrm{c}}-\mathrm{c})$$ $$\Rightarrow \mathrm{the}\mathrm{solution}\mathrm{is}6$$

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