Question

Daca a=3-√5 si b=3+√5,calculati (a-b+2√5-1)la puterea 2008 ; daca a=√150+√216-√294 si b=√48-√75+√147, calculati a supra b

Answer 1

$\frac{5\sqrt{6}+6\sqrt{6}-7\sqrt{6}}{4\sqrt{3}-5\sqrt{3}+7\sqrt{3}}= \frac{\sqrt{6}(5+6-7)}{\sqrt{3}(4-5+7)}= \frac{4\sqrt{6}}{6\sqrt{3}}= \frac{4\sqrt{18}}{18}= \frac{12\sqrt{2}}{18}= \frac{2\sqrt{2}}{3}$$(3- \sqrt{5} -3- \sqrt{5} +2 \sqrt{5} -1)^{2008)=(-2 \sqrt{5}+2 \sqrt{5}-1)^{2008}=(-1)^{2008}=1$