Question Number 192134 by mustafazaheen last updated on 09/May/23
$$\mathrm{when}\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{7}} =\sqrt{\mathrm{57125}}+\sqrt{\mathrm{57124}} \\ $$$$\mathrm{then}\:\:\:\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{7}} =? \\ $$
Answered by som(math1967) last updated on 09/May/23
$$\:\:\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)=\mathrm{1} \\ $$$$\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)=\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)} \\ $$$$\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{7}} =\frac{\mathrm{1}}{\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{7}} }=\frac{\mathrm{1}}{\:\sqrt{\mathrm{57125}}+\sqrt{\mathrm{57124}}} \\ $$$$\:\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{7}} =\frac{\sqrt{\mathrm{57125}}−\sqrt{\mathrm{57124}}}{\mathrm{57125}−\mathrm{57124}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\sqrt{\mathrm{57125}}−\sqrt{\mathrm{57124}} \\ $$
Commented by mustafazaheen last updated on 09/May/23
$$\:\cancel{\lesseqgtr} \\ $$