Question

Xét dấu của các biểu thức sau:

A=x²-2x+15

B=4a²-4a+23

C=2x²-7x+37

D=4x-9x²-17

Answer 1

\(a=x^2-2x+15=x^2-2x+1+14=\left(x-1\right)^2+14>0\)

\(b=4a^2-4a+23=4a^2-4a+4+19=\left(2a-2\right)^2+19>0\)

\(c=2x^2-7x+37=2\left(x^2-\dfrac{7}{2}x+\dfrac{37}{2}\right)\)

\(c=2\left(x^2-\dfrac{7}{2}x+\dfrac{49}{16}+\dfrac{247}{16}\right)\)

\(c=2\left(x^2-\dfrac{7}{2}x+\dfrac{49}{16}\right)+\dfrac{247}{8}\)

\(c=2\left(x-\dfrac{7}{4}\right)^2+\dfrac{247}{8}>0\)

\(d=4x-9x^2-17=-9x^2+4x-17\)

\(d=-9x^2+4x-\dfrac{4}{9}-\dfrac{149}{9}\)

\(d=-\left(9x^2-4x+\dfrac{4}{9}\right)-\dfrac{149}{9}\)

\(d=-\left(3x-\dfrac{2}{3}\right)^2-\dfrac{149}{9}< 0\)