Đáp án:
$\\$
`Q = 5x^2 - 10x`
`⇔ Q = 5x^2 - 10x + 5-5`
`⇔ Q = 5 (x^2 - 2x + 5)-5`
`⇔ Q = 5 (x^2 - 2x + 1 - 5`
`⇔ Q = 5 (x^2 - 2x . 1 + 1^2 ) - 5`
`⇔ Q= 5 (x-1)^2 -5`
Với mọi `x` có : `(x-1)^2 ≥0`
`⇔ 5 (x-1)^2 ≥0∀x`
`⇔ 5 (x-1)^2-5 ≥ -5∀x`
`⇔ Q ≥ -5 ∀x`
`⇔ min Q = -5`
Dấu "`=`" xảy ra khi :
`⇔x-1=0`
`⇔x=0+1`
`⇔x=1`
Vậy `min Q =-5 ⇔ x=1`
$Q=5x^2-10x$
$= 5x^2-10x+5-5$
$= 5(x^2-2x+1)-5$
$= 5(x-1)^2-5$
Vì $5(x-1)^2\ge 0\; \forall x$
$\to 5(x-1)^2-5 \ge -5\; \forall x$
Vậy $\min Q=-5$ khi $x-1=0 ↔ x=1$
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