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Question Number 27718 by mondodotto@gmail.com last updated on 13/Jan/18

Answered by prakash jain last updated on 13/Jan/18

$${\left(\sqrt{2+\sqrt{3}}\right)}^x=a$$$${\left(\sqrt{2-\sqrt{3}}\right)}^x=\frac{1}{a}$$$$a+\frac{1}{a}=4\Rightarrow a^2-4a+1=0$$$$a=\frac{4\pm \sqrt{12}}{2}=2\pm \sqrt{3}$$$${\left(\sqrt{2+\sqrt{3}}\right)}^x=(2\pm \sqrt{3})$$$${\left(\sqrt{2+\sqrt{3}}\right)}^x=(2+\sqrt{3})\Rightarrow x=2$$$${\left(\sqrt{2+\sqrt{3}}\right)}^x=(2-\sqrt{3})\Rightarrow x=-2$$$$x=\pm 2$$

Commented by mondodotto@gmail.com last updated on 13/Jan/18

$$\mathrm{thanx}\mathrm{a}\mathrm{lot}\mathrm{sir}$$

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