Question

Tính: √(a+2√a−1) +√(a−2√a−1) 

Help me, Please........!!!!!!!!!

Answer 1

ĐK a>= 1

Đặt A = \(\sqrt{a+2\sqrt{a-1}}\)+ \(\sqrt{a-2\sqrt{a-1}}\)

= \(\sqrt{a-1+2\sqrt{a-1}+1}\)+ \(\sqrt{a-1-2\sqrt{a-1}+1}\)

= \(\sqrt{\left(\sqrt{a-1}+1\right)^2}\)+ \(\sqrt{\left(\sqrt{a-1}-1\right)^2}\)

= \(\sqrt{a-1}\)+ 1 + |\(\sqrt{a-1}\)- 1|

Nếu a>=2 thì A = \(\sqrt{a-1}\)+1 + \(\sqrt{a-1}\)-1 = 2\(\sqrt{a-1}\)

Nếu a < 2 thì A= \(\sqrt{a-1}\)+ 1 +1 - \(\sqrt{a-1}\)=2