CMR các biểu thức sau luôn dương voi mọi x 1, C=(x+3)(x-11)+2008 2 F= x^2y^2-6xy+4y^2 -4y +10 01/07/2021 Bởi Abigail CMR các biểu thức sau luôn dương voi mọi x 1, C=(x+3)(x-11)+2008 2 F= x^2y^2-6xy+4y^2 -4y +10
Đáp án: `1, C=(x+3)(x-11)+2008` `C=x^2+3x-11x-33+2008` `C=x^2-8x+1975` `C=x^2-2.x.4+16+1959` `C=(x-4)^2+1959>=1959>0` `(đpcm)` `2, F=x^2y^2-6xy+4y^2-4x+10` `F=(x^2y^2-2.xy.3+9)+(4x^2-4x+1)` `F=(xy-3)^2+(2x-1)^2>=0` `(đpcm)` Bình luận
`1)` `C=(x+3)(x-11)+2008` `C=x^2+3x-11x-33+2008` `C=x^2-8x+1975` `C=x^2-2.x.4+16+1959` `C=(x-4)^2+1959` $\geq$ `1959>0` `(đpcm)` `2)` `F=x^2y^2-6xy+4y^2-4x+10` `F=(x^2y^2-2.xy.3+9)+(4x^2-4x+1)` `F=(xy-3)^2+(2x-1)^2` $\geq$ `0` `(đpcm)` Bình luận
Đáp án:
`1, C=(x+3)(x-11)+2008`
`C=x^2+3x-11x-33+2008`
`C=x^2-8x+1975`
`C=x^2-2.x.4+16+1959`
`C=(x-4)^2+1959>=1959>0` `(đpcm)`
`2, F=x^2y^2-6xy+4y^2-4x+10`
`F=(x^2y^2-2.xy.3+9)+(4x^2-4x+1)`
`F=(xy-3)^2+(2x-1)^2>=0` `(đpcm)`
`1)`
`C=(x+3)(x-11)+2008`
`C=x^2+3x-11x-33+2008`
`C=x^2-8x+1975`
`C=x^2-2.x.4+16+1959`
`C=(x-4)^2+1959` $\geq$ `1959>0` `(đpcm)`
`2)`
`F=x^2y^2-6xy+4y^2-4x+10`
`F=(x^2y^2-2.xy.3+9)+(4x^2-4x+1)`
`F=(xy-3)^2+(2x-1)^2` $\geq$ `0` `(đpcm)`