Question

Answer 1

`P=2x^2 -4x+5`

`P=2(x^2 -2x +5/2)`

`P=2(x^2 -2.x.1 +1 -1 +5/2)`

`P=2[(x-1)^2 +3/2]≥3` với mọi `x`

Vì `(x-1)^2 ≥0` với mọi `x`

Dấu "=" xảy ra khi `x-1=0=>x=1`

Vậy \(P_{min}\) là:`3` khi `x=1`

Answer 2

\(P=2\left(x^2-2x+1\right)+3=2\left(x-1\right)^2+3\)

Do \(\left(x-1\right)^2\ge0;\forall x\)

\(\Rightarrow P\ge3;\forall x\)

\(P_{min}=3\) khi \(x=1\)