Question

Cho 2(a + 1)(b + 1) = (a + b)(a + b +2). CMR: \(a^2\)+ \(b^2\) = 2

Answer 1

\(2\left(a+1\right)\left(b+1\right)=\left(a+b\right)\left(a+b+2\right)\)

\(\Leftrightarrow2ab+2a+2b+2=a^2+2ab+b^2+2a+2b\)

\(\Leftrightarrow a^2+b^2=2\left(đfcm\right)\)

Answer 2

`-> 2a + 2b + 2ab + 2 = a^2 + ab + 2a + ba + b^2 + 2b`

`-> (2a-2a) + (2b-2b) + (2ab - 2ab) + 2 = a^2 + b^2`

`=> a^2 + b^2 = 2`.