Question

chứng minh rằng a)2*(a²+b²)=(a+b)²thì a=b

                             b)(a²+b²)*(x²+y²)=(ax+by)² thì ay=bx

giúp với ạ

Answer 1

a)

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

\(=>2X\left(x^2+b\right)\)

Chứng minh 

A=min a2 + b =........

Câu b tương tự 

Answer 2

a) \(2.\left(a^2+b^2\right)=\left(a+b\right)^2\Leftrightarrow2.\left(a^2+b^2\right)-\left(a+b\right)^2=0\)

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

Answer 3

b) \(\Leftrightarrow a^2x^2+a^2y^2+b^2x^2+b^2y^2=a^2x^2+2axby+b^2y^2\)

    \(\Leftrightarrow a^2y^2+b^2x^2=2axby\)

    \(\Leftrightarrow\left(ay\right)^2+\left(bx\right)^2-2axby=0\Leftrightarrow\left(ay-bx\right)^2=0\)

    \(\Leftrightarrow ay-bx=0\Leftrightarrow ay=bx\)