x/a+y/b+z/c=1, a/x+b/y+c/z=0 tính x^2/a^2 + y^2/b^2 + z^2/c^2 17/09/2021 Bởi Adalynn x/a+y/b+z/c=1, a/x+b/y+c/z=0 tính x^2/a^2 + y^2/b^2 + z^2/c^2
Ta có: `a/x+b/y+c/z=0` `⇒ayz+bxz+cxy=0` Ta có: ` x/a+y/b+z/c=1` `⇔(x/a+y/b+z/c)^2=1` `⇔x^2/a^2+y^2/b^2+z^2/c^2+2((xy)/(ab)+(yz)/(bc)+(zx)/(ca))=1` `⇔x^2/a^2+y^2/b^2+z^2/c^2+2((ayz+bxz+cxy)/(abc))=1` `⇔x^2/a^2+y^2/b^2+z^2/c^2+2.0=1` `⇔x^2/a^2+y^2/b^2+z^2/c^2=1` `⇒ĐPCM` Bình luận
Đáp án:
Giải thích các bước giải:
Ta có:
`a/x+b/y+c/z=0`
`⇒ayz+bxz+cxy=0`
Ta có:
` x/a+y/b+z/c=1`
`⇔(x/a+y/b+z/c)^2=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2+2((xy)/(ab)+(yz)/(bc)+(zx)/(ca))=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2+2((ayz+bxz+cxy)/(abc))=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2+2.0=1`
`⇔x^2/a^2+y^2/b^2+z^2/c^2=1`
`⇒ĐPCM`