Đáp án:
`A=4022`
Giải thích các bước giải:
`A=xsqrt{((2011+y^2)(2011+z^2))/(2011+x^2)}+ysqrt{((2011+x^2)(2011+z^2))/(2011+y^2)}+zsqrt{((2011+y^2)(2011+x^2))/(2011+z^2)}`
`+)2011+y^2`
`=y^2+xy+yz+zx`
`=y(x+y)+z(x+y)`
`=(x+y)(y+z)`
`CMT^2` ta cũng có
`2011+x^2`
`=(x+y)(x+z)`
`2011+z^2`
`=(y+z)(z+x)`
`=> A=xsqrt{((2011+y^2)(2011+z^2))/(2011+x^2)}+ysqrt{((2011+x^2)(2011+z^2))/(2011+y^2)}+zsqrt{((2011+y^2)(2011+x^2))/(2011+z^2)}`
`=xsqrt{((x+y)(y+z)(y+z)(z+x))/((x+y)(x+z))}+ysqrt{((x+y)(x+z)(y+z)(z+x))/((x+y)(y+z))}+zsqrt{((x+y)(y+z)(x+y)(z+x))/((y+z)(x+z))}`
`=xsqrt{(y+z)^2}+ysqrt{(x+z)^2}+zsqrt{(x+y)^2}`
`=x(y+z)+y(x+z)+z(y+x)`
`=xy+xz+xy+yz+zy+xz`
`=2(xy+yz+zx)`
`=2.2011`
`=4022`
Vậy `A=4022`
$@Kate2007$
