Đáp án:
`P=a^2+b^2+1/a^2+1/b^2`
`=a^2+1/(16a^2)+b^2+1/(16b^2)+15/16(1/a^2+1/b^2)`
Áp dụng bđt cosi ta có:
`P>=2\sqrt{1/16}+2\sqrt{1/16}+15/16*8/(a+b)^2`
`<=>P>=2*1/4+2*1/4+15/16*8`
`<=>P>=1/2+1/2+15/2`
`<=>P>=1+15/2=17/2`.
Dấu "=" xảy ra khi `a=b=1/2.`