Question

Упростить выражение.

Answer 1

$\sqrt{a+3-4 \sqrt{a-1} }- \sqrt{ a+8-6\sqrt{a-1} }-?\\ a\ \textgreater \ 10\\\\ \sqrt{a-1}=t\\a-1=t^2\\a=t^2+1\\\\ \sqrt{t^2+1+3-4t}- \sqrt{t^2+1+8-6t}= \sqrt{t^2-4t+4}- \sqrt{t^2-6t+9}=\\= \sqrt{(t-2)^2}- \sqrt{(t-3)^2}=|t-2|-|t-3|\\\\| \sqrt{a-1}-2|-| \sqrt{a-1}-3|=\sqrt{a-1}-2-\sqrt{a-1}+3=3-2=1$