Question

6(x-1)²=(2+√10)$\sqrt{14-2 \sqrt{40} }$
eu am continuat cu 6(x-1)²=(2+√10)$\sqrt{(2- \sqrt{10} )^2}$
6(x-1²)=(2+√10)(-2+√10)
si mai departe nu stiu sa fac...aici m-am blocat...putin ajutor?

Answer 1

[tex]6(x-1)^2=(2+\sqrt{10})\sqrt{14-2\sqrt{40}}\\ 2\sqrt{40}=2\sqrt{4\cdot10}=2\cdot2\sqrt{10}=4\sqrt{10}\\ \sqrt{14-4\sqrt{10}}=\sqrt{10+4-4\sqrt{10}}=\sqrt{(2-\sqrt{10})^2}=|2-\sqrt{10}|=\\= \sqrt{10}-2\\ Revenind:6(x-1)^2=(2+\sqrt{10})(\sqrt{10}-2)\\ 6(x-1)^2=10-4\\ 6(x-1)^2=6|:6\\ (x-1)^2=1\\ |x-1|=1\\ Si\ de\ aici\ avem\ cele\ doua\ solutii....[/tex]