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Question Number 94855 by mathocean1 last updated on 21/May/20

$$\mathrm{Solve}\mathrm{for}\mathrm{x}\mathrm{in}\mathbb{R}$$$$x\sqrt{x+3}-4\sqrt{x+3}+2x-8=0$$

Answered by ElOuafi last updated on 21/May/20

$$let;x⩾-3then$$$$x\sqrt{x+3}-4\sqrt{x+3}+2x-8=0$$$$\iff (x-4)\sqrt{x+3}+2(x-4)=0$$$$\iff (x-4)(\sqrt{x+3}+2)=0$$$$\iff x-4=0or\sqrt{x+3}+2=0$$$$\Rightarrow x=4because\sqrt{x+3}+2>0\mathrm{\forall }x\in \mathbb{R}$$$$sothesolutionis4$$

Commented by mathocean1 last updated on 21/May/20

$$\mathrm{Thank}\mathrm{you}\mathrm{sir}!$$

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