Giải thích các bước giải:
a) Ta có:
`x/y+y/x=(x^2+y^2)/(xy)=((x^2-2xy+y^2)+2xy)/(xy)`
`=(x-y)^2/(xy)+2`
Có `(x+y)^2>=0`
Mà `x;y` cùng dấu
`=>xy>0=>(x-y)^2/(xy)>=0`
`=>(x-y)^2/(xy)+2>=2`
Vậy `x/y+y/x>=2.`
b) `P=x^2/y^2+y^2/x^2-3(x/y+y/x)+5`
`=x^2/y^2+2+y^2/x^2-3(x/y+y/x)+3`
`=(x^2/y^2+2. x/y . y/x+y^2/x^2)-3(x/y+y/x)+3`
`=(x/y+y/x)^2-2(x/y+y/x).3/2+9/4+3/4`
`=(x/y+y/x-3/2)^2+3/4`
`=>Pmin=3/4`
`<=>x/y+y/x-3/2=0`
`=>(x^2+y^2)/(xy)=3/2`
`=>2(x^2+y^2)=3xy`
`=>2x^2-4xy+2y^2=-xy`
`=>2(x-y)^2=-xy`
`=>x=y=0`
Vậy `Pmin=3/4<=>x=y=0.`
