tìm min x^2+5x+23 x^2+6x+30 x^2+7x+34 x^3+3x^2+5x 29/10/2021 Bởi Ayla tìm min x^2+5x+23 x^2+6x+30 x^2+7x+34 x^3+3x^2+5x
Đáp án: a, ⇔x^2+5/2*2*x+25/4-25/4+23 ⇔(x+5/2)^2+67/4 mà (x+5/2)^2≥0.∀x ⇒MIN=67/4⇔X=-5/2 b, ⇔x^2+2*3*x+9+21 ⇔(x+3)^2+21 mà (x+3)^2≥0.∀x ⇒MIN=21⇔X=-3 c, ⇔x^2+7/2*2*x+49/4-49/4+34 ⇔(x+7/2)^2+87/4 mà (x+7/2)^2≥0.∀x ⇒MIN=87/4⇔X=-7/2 d, ⇔x(x^2+3x+5) ⇔x[(x^2+3/2*2*x+9/4)-9/4+5] ⇔x[(x+3/2)^2+11/4] Bình luận
Giải thích các bước giải: `a,` `⇔x^2+5/2.2.x+25/4-25/4+23` `⇔(x+5/2)^2+67/4` mà `(x+5/2)^2≥0.∀x` `⇒MIN=67/4` `⇔X=-5/2` `b,` `⇔x^2+2.3.x+9+21` `⇔(x+3)^2+21` mà `(x+3)^2≥0.∀x` `⇒MIN=21` `⇔X=-3` `c,` `⇔x^2+7/2.2.x+49/4-49/4+34` `⇔(x+7/2)^2+87/4` mà `(x+7/2)^2≥0.∀x` `⇒MIN=87/4` `⇔X=-7/2` `d,` `⇔x(x^2+3x+5)` `⇔x[(x^2+3/2.2.x+9/4)-9/4+5]` `⇔x[(x+3/2)^2+11/4]` Bình luận
Đáp án:
a,
⇔x^2+5/2*2*x+25/4-25/4+23
⇔(x+5/2)^2+67/4
mà (x+5/2)^2≥0.∀x
⇒MIN=67/4⇔X=-5/2
b,
⇔x^2+2*3*x+9+21
⇔(x+3)^2+21
mà (x+3)^2≥0.∀x
⇒MIN=21⇔X=-3
c,
⇔x^2+7/2*2*x+49/4-49/4+34
⇔(x+7/2)^2+87/4
mà (x+7/2)^2≥0.∀x
⇒MIN=87/4⇔X=-7/2
d,
⇔x(x^2+3x+5)
⇔x[(x^2+3/2*2*x+9/4)-9/4+5]
⇔x[(x+3/2)^2+11/4]
Giải thích các bước giải:
`a,`
`⇔x^2+5/2.2.x+25/4-25/4+23`
`⇔(x+5/2)^2+67/4`
mà `(x+5/2)^2≥0.∀x`
`⇒MIN=67/4`
`⇔X=-5/2`
`b,`
`⇔x^2+2.3.x+9+21`
`⇔(x+3)^2+21`
mà `(x+3)^2≥0.∀x`
`⇒MIN=21`
`⇔X=-3`
`c,`
`⇔x^2+7/2.2.x+49/4-49/4+34`
`⇔(x+7/2)^2+87/4`
mà `(x+7/2)^2≥0.∀x`
`⇒MIN=87/4`
`⇔X=-7/2`
`d,`
`⇔x(x^2+3x+5)`
`⇔x[(x^2+3/2.2.x+9/4)-9/4+5]`
`⇔x[(x+3/2)^2+11/4]`