`B=4x^2+5x-2`
`=4(x^2 +5/4x)-2`
`=4(x^2 +2. 5/8x+25/64-25/64)-2`
`=4(x+5/8)^2-25/16-2`
`=4(x+5/8)^2-57/16`
Do `4(x+5/8)^2>=0`
`=>4(x+5/8)^2-57/16>=-57/16`
Dấu `'='` xảy ra `<=>x+5/8=0`
`<=>x=-5/8`
Vậy Min `B=-57/16<=>x=-5/8`
`C=-2x^2+5x-1`
`=-2(x^2 -5/2x)-1`
`=-2(x^2-2.5/4x+25/16-25/16)-1`
`=-2(x-5/4)^2 +17/8`
Do `-2(x-5/4)^2<=0AAx`
`=>-2(x-5/4)^2+17/8<=17/8`
`<=>C<=17/8`
Dấu `'='` xảy ra `<=>x-5/4=0`
`<=>x=5/4`
Vậy `MaxC=17/8<=>x=5/4`
a) B=4x^2+5x-2
= 4x^2 +\(\dfrac{1}{2}\cdot5\cdot2x+\dfrac{1}{4}-\dfrac{9}{4}\)
= (2x+\(\dfrac{1}{2}\))^2-\(\dfrac{9}{4}\ge\dfrac{-9}{4}\)
dấu bằng xảy ra khi x=\(\dfrac{-1}{4}\)
tương tự mà làm nhé
`a)`
`B=4x^2+5x-2`
`B=4x^2+2.2x.5/4+25/16-57/16`
`B=(2x+5/4)^2-57/16`
Vì `(2x+5/4)^2 >= 0 AA x`
`<=>(2x+5/4)^2-57/16 >= -57/16 AA x`
Hay `B >= -57/16 AA x`
Dấu "`=`" xảy ra`<=>(2x+5/4)^2=0<=>x=-5/8`
Vậy `GTN N` của `B` là `-57/16` khi `x=-5/8`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`b)`
`C=-2x^2+5x-1`
`C=-2(x^2-5/2x+1/2)`
`C=-2(x^2-2.x. 5/4+25/16-17/16)`
`C=-2(x-5/4)^2+17/8`
Vì `-2(x-5/4)^2 <= 0 AA x`
`<=>-2(x-5/4)^2+17/8 <= 17/8 AA x`
Hay `C <= 17/8 AA x`
Dấu "`=`" xảy ra`<=>(x-5/4)^2=0<=>x=5/4`
Vậy `GTLN` của `C` là `17/8` khi `x=5/4`
`a, (2x)^2 + 2 . 2 . 5/4 + 25/16 - 57/16`
`= (2x + 5/4)^2 - 57/16 >= 0 - 57/16 = -57/16`.
Dấu bằng xảy ra `<=> x = -5/8`
`b, = -2(x^2 - 5/2 x + 1/2)`
`= -2(x^2 - 2 . 5/4 + 25/16 - 17/16)`
`= -2(x-5/4)^2 + 17/8 <= 0 + 17/8 = 17/8`