Question

√а+2√а+3+4+√а-2√а+3+4=

Answer 1

$sqrt{a+2sqrt{a+3}+4}+sqrt{a-2sqrt{a+3}+4}=\\=sqrt{(sqrt{a+3}+1)^2}+sqrt{(sqrt{a+3}-1)^2}=\\=|underbrace {sqrt{a+3}+1}_{>0}|+|sqrt{a+3}-1|=sqrt{a+3}+1+|sqrt{a+3}-1|=\\=left { {{2sqrt{a+3}; ,; esli; ageq -2; ,} atop {2; ,; esli; a<-2; .qquad ; ; }} right.$

$star ; ; |sqrt{a+3}-1|=sqrt{a+3}-1; ,; ; esli; sqrt{a+3}-1geq 0; ,; sqrt{a+3}geq 1; to \\a+3geq 1; ,; ageq -2; ; star \\star |sqrt{a+3}-1|=1-sqrt{a+3}; ,; esli; sqrt{a+3}-1<0; ,; sqrt{a+3}<1; to \\a+3<1; ,; a<-2; ; star$