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Question Number 187874 by mustafazaheen last updated on 23/Feb/23

$$howissolution$$$${(\sqrt{2}-1)}^{13}=\mathrm{x}{(\sqrt{2}+1)}^{221}=?$$$$1){\mathrm{x}}^{-16}2){\mathrm{x}}^{-17}3){\mathrm{x}}^{221}4){\mathrm{x}}^{21}$$

Answered by som(math1967) last updated on 23/Feb/23

$$(\sqrt{2}+1)(\sqrt{2}-1)=1$$$$\Rightarrow (\sqrt{2}-1)=\frac{1}{\sqrt{2}+1}$$$${(\sqrt{2}-1)}^{13}=x$$$$\Rightarrow \frac{1}{{(\sqrt{2}+1)}^{13}}=x$$$$\Rightarrow {(\sqrt{2}+1)}^{13}=\frac{1}{x}$$$$\Rightarrow {\left\{{(\sqrt{2}+1)}^{13}\right\}}^{17}=\frac{1}{x^{17}}$$$${(\sqrt{2}+1)}^{221}=x^{-17}$$

Answered by Sutrisno last updated on 23/Feb/23

$${(\sqrt{2}+1)}^{221}.\frac{{(\sqrt{2}-1)}^{221}}{{(\sqrt{2}-1)}^{221}}$$$$=\frac{1}{{\left({(\sqrt{2}-1)}^{13}\right)}^{17}}$$$$=\frac{1}{x^{17}}$$$$=x^{-17}$$

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