Câu hỏi của Vân Anh Chu

Question

1,chứng tỏ

a,x mũ2 -x+1>0 với mọi x

b,25x mũ2 +10x+2>0 với mọi x

c,3x mũ2+2x+14>0 với mọi x

d,2x mũ2+y mũ2+ 2xy- 2x+2>0 với mọi x

2,tìm giá trị nhỏ nhất của

A=3x mũ2-3x

B=...

Hắc Hường · Accepted Answer

Bài 1:

a) $x^2-x+1$

$=x^2-x+\dfrac{1}{4}+\dfrac{3}{4}$

$=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}>0;\forall x$

b) $25x^2+10x+2$

$=25x^2+10x+1+1$

$=\left(5x+1\right)^2+1\ge1>0;\forall x$

c) $3x^2+2x+14$

$=3x^2+2x+\dfrac{1}{3}+\dfrac{41}{3}$

$=\left(\sqrt{3}x+\dfrac{\sqrt{3}}{3}\right)^2+\dfrac{41}{3}\ge\dfrac{41}{3}>0;\forall x$

d) $2x^2+y^2-2xy-2x+2$

$=x^2+y^2-2xy-2x+x^2+1+1$

$=\left(x-y\right)^2+\left(x-1\right)^2+1\ge1>0;\forall x$

Vậy ...Câu trả lời: Bài 1: