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Question Number 192134 by mustafazaheen last updated on 09/May/23

$$\mathrm{when}{(\sqrt{2}+1)}^7=\sqrt{57125}+\sqrt{57124}$$$$\mathrm{then}{(\sqrt{2}-1)}^7=?$$

Answered by som(math1967) last updated on 09/May/23

$$(\sqrt{2}-1)(\sqrt{2}+1)=1$$$$(\sqrt{2}-1)=\frac{1}{(\sqrt{2}+1)}$$$${(\sqrt{2}-1)}^7=\frac{1}{{(\sqrt{2}+1)}^7}=\frac{1}{\sqrt{57125}+\sqrt{57124}}$$$${(\sqrt{2}-1)}^7=\frac{\sqrt{57125}-\sqrt{57124}}{57125-57124}$$$$=\sqrt{57125}-\sqrt{57124}$$

Commented by mustafazaheen last updated on 09/May/23

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