Question

Va rog sa ma ajutati , este urgent. Dau coroana !

Answer 1

Răspuns:

$(\sqrt{\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}} +\sqrt{\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}} +\sqrt{\frac{\sqrt{3}-1}{\sqrt{3}+1}}} ):\frac{2\sqrt{2}}{\sqrt{14}+\sqrt{2}} =$

$=(\sqrt{\frac{\sqrt{7}-\sqrt{5})\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}} +\sqrt{\frac{\sqrt{5}-\sqrt{3})\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}} +\sqrt{\frac{\sqrt{3}-1)\sqrt{3}-1}{\sqrt{3}+1}}} ):\frac{2\sqrt{2}}{\sqrt{2}(\sqrt{7}+1)} =$

$=(\sqrt{\frac{(\sqrt{7}-\sqrt{5})^{2} }{7-5}}+\sqrt{\frac{(\sqrt{5}-\sqrt{3})^{2} }{5-3}}+\sqrt{\frac{(\sqrt{3}-1)^{2} }{3-1}})*\frac{\sqrt{7}+1}{2}=$

$=\frac{\sqrt{7}-\sqrt{5}+\sqrt{5}-\sqrt{3}+\sqrt{3}-1}{\sqrt{2}} *\frac{\sqrt{7}+1}{2} =$

$=\frac{(\sqrt{7}-1)(\sqrt{7}+1)}{2\sqrt{2}} =\frac{\sqrt{2})7-1}{2\sqrt{2}} =\frac{6\sqrt{2}}{4}=\frac{3\sqrt{2}}{2}$

Explicație pas cu pas:

Pentru rezolvarea acestui exercitiu se foloseste formula de calcul prescurtat:

(a+b)(a-b)=a²-b²