Question

CMR:

a) 4x²-x+1>0

b) -3x²+x-1<0

Answer 1

a,4x²- x + 1 = (2x)² - 2.2x.0,25 + 0,0625 + 0,975 = (2x - 0.25)² + 0,975 > 0 

b, -( 3x² - x + 1) rồi chứng minh tương tự

Answer 2

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

\(=-\left[\left(\sqrt{3}x\right)^2-2.\sqrt{3}x.\frac{1}{2\sqrt{3}}+\frac{1}{12}+\frac{11}{12}\right]\)

\(=-\left[\left(\sqrt{3}x-\frac{1}{2\sqrt{3}}\right)^2+\frac{11}{12}\right]\)

\(=-\left(\sqrt{3}x-\frac{1}{2\sqrt{3}}\right)^2-\frac{11}{12}< 0\left(đpcm\right)\)