1: \(M=4x-x^2+3\)
\(=-\left(x^2-4x-3\right)\)
\(=-\left(x^2-4x+4-7\right)\)
\(=-\left(x-2\right)^2+7< =7\forall x\)
Dấu '=' xảy ra khi x-2=0
=>x=2
2: \(N=x-x^2\)
\(=-\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{1}{4}\)
\(=-\left(x-\dfrac{1}{2}\right)^2+\dfrac{1}{4}< =\dfrac{1}{4}\forall x\)
Dấu '=' xảy ra khi \(x-\dfrac{1}{2}=0\)
=>\(x=\dfrac{1}{2}\)
3: \(P=2x-2x^2-5\)
\(=-2\left(x^2-x+\dfrac{5}{2}\right)\)
\(=-2\left(x^2-x+\dfrac{1}{4}+\dfrac{9}{4}\right)\)
\(=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}< =-\dfrac{9}{2}\forall x\)
Dấu '=' xảy ra khi \(x-\dfrac{1}{2}=0\)
=>\(x=\dfrac{1}{2}\)
`a)M = 4x - x^2 + 3`
`=-x^2 +4x+3`
`=-(x^2 - 4x -3)`
`=-(x^2 -2x2+4-7)`
`=-[(x-2)^2+(-7)]
`=-(x-2)^2 + 7`
Ta thấy `(x-2)^2 >=0`\(\forall x\)
`-(x-2)^2<=0`\(\forall x\)
`-(x-2)^2 + 7<=0`\(\forall x\)
Dấu `"="` xảy ra `<=>x-2 =0`
`<=>x=2`
`N=x - x^2`
`=-x^2+x`
`=-(x^2-x)`
`=-(x^2-2x.1/2 + 1/4 -1/4)`
`=-[(x-1/2)^2 - 1/4]`
`=-(x-1/2)^2 +1/4`
ta thấy :
`(x-1/2)^2>=0`\(\forall x\)
`-(x-1/2)^2<=0`\(\forall x\)
`-(x-1/2)^2 + 1/4<=0\(\forall x\)
Dấu `"="` xảy ra `<=>x-1/2 =0`
`<=> x=1/2`
`P=2x-2x^2-5`
`=-2x^2+2x-5`
`=-2(x^2 -x + 5/2)`
`=-2(x^2 -2x.1/2 +1/4 +9/4)`
`=-2[(x-1/2)^2 + 9/4]`
`=-2(x-1/2)^2 - 9/2`
Dấu `"="` xảy ra `<=>x-1/2 =0`
`<=>x=1/2`
