Ta có:

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

\(=a^2x^2-2abxy+b^2y^2+a^2y^2+2abxy+b^2x^2\) \(=\left(ax-by\right)^2+\left(ay+bx\right)\)

\(=vp\)

\(\Rightarrowđpcm\)

Phương Ann Nhã Doanh đề bài khó wá Mashiro Shiina Đinh Đức Hùng

Nguyễn Huy Tú Lightning Farron Akai Haruma

Ta có :

A= ax+ay+bx+by+x+y

= a(x+y)+b(x+y)+x+y

= (a+b+1)(x+y)

= (\(\dfrac{1}{3}\)+1).\(\dfrac{-9}{4}\)

= \(\dfrac{4}{3}.\dfrac{-9}{4}\)

= -3

B= ax+ay-bx-by-x-y

= a(x+y)-b(x+y)-(x+y)

= (a-b-1)(x+y)

= (\(\dfrac{1}{2}\)-1).\(\dfrac{1}{2}\)

= \(\dfrac{-1}{2}.\dfrac{1}{2}\)

= \(\dfrac{-1}{4}\)

a) \(ax+ay+bx+by=a\left(x+y\right)+b\left(x+y\right)=\left(a+b\right)\left(x+y\right)=\left(-2\right).17=-34\)

b) \(ax-ay+bx-by=a\left(x-y\right)+b\left(x-y\right)=\left(a+y\right)\left(x-y\right)=\left(-7\right).\left(-1\right)=7\)

Bằng shit

nhjjfkjnkorkgbklklflfjkbknkm

A,=a.(x+y)+b.(x+y)

    =(x+y).(a+B)

    =17.(-2)

    =-34

a)   suy ra a.(x+y)+b.(x+y)

      suy ra (x+y) (a+b)

      suy ra 17. (-2) = 34

b)    suy ra    a.(x-y) + b.(x-y)

       suy ra (a+b) (x-y)

       suy ra (-7).(-1)

 mk làm bậy ko bít đúng hay ko

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 \(\dfrac{a}{x}=\dfrac{b}{y}\)