Question

1,chứng minh biểu thức luôn dương vs mọi biến

A=3x^2 - 5x + 3

B=2x^2 + 3x + 4

C=x^2 + 3x + 5

D=x^2 + 30 + 6y + 9y^2 - 10x

E=16x^2 + 6 + 8x - 4y + y^2

2,chứng minh biểu thức luôn âm vs mọi biến

M= -x^2 - 7x - 15

N=6x - 5x^2 - 10

C=4x - 1/3x^2 - 7

D= -5x^2 + 7x - 9

Answer 1

\(A=3\left(x-\frac{5}{6}\right)^2+\frac{11}{12}\)

\(B=2\left(x-\frac{3}{4}\right)^2+\frac{23}{8}\)

\(C=\left(x+\frac{3}{2}\right)^2+\frac{11}{4}\)

\(D=\left(x-5\right)^2+\left(3y+1\right)^2+4\)

\(E=\left(4x+1\right)^2+\left(y-2\right)^2+1\)

\(M=-\left(x+\frac{7}{2}\right)^2-\frac{11}{4}\)

\(N=-5\left(x-\frac{3}{5}\right)^2-\frac{41}{5}\)

\(C\) đề sai ví dụ \(x=3\Rightarrow C=2>0\)

\(D=-5\left(x-\frac{7}{10}\right)^2-\frac{131}{20}\)