bn nào viết rõ hơn giùm mik đc ko.
(a^2+b^2)(x^2+y^2)=(ax+by)^2
<=> a^2x^2 + a^2y^2 + b^2x^2 + b^2y^2 = a^2x^2 + 2abxy + b^2y^2
<=> a^2y^2 + b^2x^2 = 2abxy
<=> a^2y^2 + b^2x^2 - 2abxy = 0
<=> (ay - bx)^2 = 0
=> ay - bx = 0
=> ay = bx
=> a/x = b/y ( x,y khác 0)
Ta có: \(\left(ax+by\right)^2=\left(a^2+b^2\right)\left(x^2+y^2\right)\)
\(\Leftrightarrow a^2x^2+2abxy+b^2y^2=a^2x^2+a^2y^2+x^2b^2+b^2y^2\)
\(\Leftrightarrow2abxy=a^2y^2+x^2b^2\)
\(\Leftrightarrow\left(ay-xb\right)^2=0\)
\(\Leftrightarrow ay=xb\)
hay \(\dfrac{a}{x}=\dfrac{b}{y}\)