Question

Cho: √a+b = √a−1+√b−1  (với a ≥ 1; b ≥ 1)

Chứng minh a + b = ab

Answer 1

ko đăng lại

Answer 2

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

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

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

\(\Leftrightarrow\sqrt{\left(a-1\right)\left(b-1\right)}=1\)

\(\Leftrightarrow\left(a-1\right)\left(b-1\right)=1\)

\(\Leftrightarrow ab-a-b+1=1\)

\(\Leftrightarrow ab-a-b=0\)

\(\Leftrightarrow a+b=ab\) ( đfcm )