Question

Chứng minh rằng nếu 2(a² + b²) = (a+b)² thì a = b.

Answer 1

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

\(\Leftrightarrow2a^2+2b^2=a^2+2ab+b^2\)

\(\Leftrightarrow a^2-2ab+b^2=0\)

\(\Leftrightarrow\left(a-b\right)^2=0\)

\(\Leftrightarrow a-b=0\)

\(\Leftrightarrow a=b\) (đpcm)

Answer 2

`2(a^2 + b^2) = (a+b)^2`

`2a^2 + 2b^2 = a^2 + 2ab + b^2`

`a^2 + b^2 = 2ab`

`-> a^2 - 2ab + b^2 = 0`

`-> (a-b)^2 = 0`

Vì `(a-b)^2 >=0 forall a, b in RR`.

`-> a - b = 0`

`-> a = b`