Question

[Fan RUNNING MAN]

A)Biết bz-cy/a=cx-az/b=ay-bx/c.Chứng minh a/x=b/y=c/z

B)Cho a,b,c,d khác 0 t/m b^2=ac;c^2=bd.Cm a^3+b^3+c^3/b^3+c^3+d^3=a/d

Answer 1

[Trà My]

Từ đề bài=>\(\frac{\left(bz-cy\right).a}{a^2}=\frac{\left(cx-az\right).b}{b^2}=\frac{\left(ay-bx\right).c}{c^2}\)

=>\(\frac{abz-acy}{a^2}=\frac{bcx-abz}{b^2}=\frac{acy-bcx}{c^2}\)

Theo t/c dãy tỉ số=nhau:

\(\frac{abz-acy}{a^2}=\frac{bcx-abz}{b^2}=\frac{acy-bcx}{c^2}=\frac{abz-acy+bcx-abz+acy-bcx}{a^2+b^2+c^2}=\frac{0}{a^2+b^2+c^2}=0\)

=>abz-acy=0.a²=0=>abz=acy=>bz=cy

bcx-abz=0.b²=0=>bcx=abz=>cx=az

acy-bcx=0.c²=0=>acy=bcx=>ay=bx

Ta có: bx=ay và bz=cy=>\(\frac{a}{x}=\frac{b}{y}=\frac{c}{z}\left(đpcm\right)\)