因式分解 1/16 x^2-3/2 x+9

解答

因式分解

\frac{1}{16} x^{2} - \frac{3}{2} x + 9

(\frac{x}{4} - 3)^{2}

求解步骤

\frac{1}{16} x^{2} - \frac{3}{2} x + 9

改写为形式

a^{2} + 2 ab + b^{2} :

\frac{x ^{2}}{16} = (\frac{1}{4} x)^{2}

9 = 3^{2}

= (\frac{1}{4} x)^{2} - \frac{3 x}{2} + 3^{2}

使用完全平方公式:

a^{2} - 2 ab + b^{2} = (a - b)^{2}

(\frac{1}{4} x)^{2} - \frac{3 x}{2} + 3^{2} = (\frac{1}{4} x - 3)^{2}

= (\frac{1}{4} x - 3)^{2}

- 6 x + 3 \geq 21

- 1.18 = \frac{0.76}{0.5} (1) + b

10 x \leq 3

∣ 3 x ∣ > 12

s im pl i f y (0.5)^{2}