Ta có x2+y2-4x+2y + 7
= ( x2 -4x+2) + ( y2+2y+1)+4
= ( x-2)2 +( y+1)2 +4
Ta có ( x-2)2 >=0 và ( y+1)2 >=0
<=> ( x-2)2 +( y+1)2 +4>=4
vậy x2+y2-4x+2y + 7>=0
phan tich da thuc sau thanh nhan tu
xy(x+y) + yz(y+z) + xz(x+z) + 2xyz
tinh gia tri bieu thuc
3(x-3)(x+7) + (x-4)2 + 48 tai x = 0,5
chung minh rang
x2 - 6x + 10 >0 voi moi x
4x - x2 - 5 <0 voi moi x
chung minh rang bieu thuc 4x(x+y)(x+y+z)(x+y) y^2x^2 luon luon khong am voi moi gia tri cua x,y va z
chung minh rang da thuc n^4-16 chia het cho 16 voi moi n la so tu nhien le
chung minh bieu thuc 2x^2-3x+7 >0 voi moi x
chung minh rang bieu thuc sau luon luon co gia tri am voi moi gia tri cua bien: -5-(x-1)(x+2)
chung minh rang 4x2- 4x+ 10>0 voi moi so thuc x
rut gon
x^2 - 4x+ 4
-2x + x^2
va tinh gia tri cua A khi x = -1/2
b) phan tich da thuc thanh nhan tu
a^3 + 8a- 4a - 8
giup minh nhe
Chung minh rang x2+5xy+2x-4xy-10y+14 >0 voi moi x,y
Cho x,y,z la cac so thuc khac 0. Thoa man : z2+z(xy-xz-yz)=0
Chung minh rang x2+(x+2y-z)2 / y2+(2x+y-z)2 = x+2y-z / 2x+y-z
cho da thuc f(x)= -2+x^4+2x^2-3x^3+4x^4-5x^4+3x^3+3 chung minh rang da thuc f(x) ko co nghiem tai moi gia tri cua x
