\(\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax+by\right)^2\)
\(\Rightarrow a^2x^2+a^2y^2+b^2x^2+b^2y^2=a^2x^2+2axby+b^2y^2\)
\(\Rightarrow a^2y^2+b^2x^2=2axby\)
\(\Rightarrow a^2y^2-2axby+b^2x^2=0\)
\(\Rightarrow\left(ay\right)^2-2.ay.bx+\left(bx\right)^2=0\)
\(\Rightarrow\left(ay-bx\right)^2=0\)
\(\Rightarrow ay-bx=0\Rightarrow ay=bx\Rightarrow\frac{a}{x}=\frac{b}{y}\)
cho x/a=y/b=z/c .hay rut gon phan thuc P=(x^2+y^2+z^2)/(ax+by+cz)^2
cho x,y,z khac 0 va \(\frac{\left(ax+by+cz\right)^2}{x^2+y^2+z^2}=a^2+b^2+c^2\)
Chung minh rang \(\frac{a}{x}=\frac{b}{y}=\frac{c}{z}\)
Cho biet x,y,z khac 0 va
\(\frac{\left(ax+by+cz\right)^2}{x^2+y^2+z^2}=a^2+b^2+c^2\)
Chung minh rang \(\frac{a}{x}=\frac{b}{y}=\frac{c}{z}\)
cho xyz khac 0 cmr neu x2-yz=a; y2-xz=b;z2-xy=c thi ax+by+cz chia het cho a+b+c
cho ax+by+cz=0 và a+b+c =2019.Tính
A=bc(x-y)^2+ac(x-z)^2+ab(x-y)^2/ax^2+by^2+cz^2
cho a+b+c = x+y+z = a/x + b/y + c/z = 0 chung minh ax^2 +by^2+cz^2 = 0
phan tich da thuc thanh nhan tu
a) 2a(x+y)+y+x
b) 2(x-y)^2-x+y
c) x^2-xy-3x+3y
d) ax^2+6x^2-6x-ax+a+b
2) phan tich da thuc thanh nhan ( nhieu phuong phap)
a) 5a^2+20a+20 c) 25-x^2+2xy-y^2
b) 5a^2-10ab+5b^2 d) m^2+2mn+n^2-p^2
phan tích da thức thanh nhan tu
a) 2a(x+y)+y+x
b) 2(x-y)^2-x+y
c) x^2-xy-3x+3y
d) ax^2+6x^2-6x-ax+a+b
2) phan tich da thuc thanh nhan tu ( nhieu phuong phap)
a) 5a^2+20a+20 c) 25-x^2+2xy-y^2
b) 5a^2-10ab+5b^2 d) m^2+2mn+n^2-p^2
Cho ax + by + cz = 0. CMR:
ax^2 + by^2 + cz^2/ bc(y-z)^2 + ca(z-x)^2 + ab(x-y)^2 = 1/a+b+c
