akar akar persamaan kuadrat : x² - 3x + 4 = 0 adalah m dan n, maka nilai dari m/n + n/m adalah

x² - 3x + 4 = 0

a = 1
b = -3
c = 4

Akar2nya m dan n
m + n = -b/a = -(-3)/1 = 3
mn = c/a = 4/1 = 4

Ditanya
[tex] \frac{m}{n} + \frac{n}{m} \\ = \frac{m^2+n^2}{mn} \\ = \frac{m^2+n^2+2mn-2mn}{mn} \\ = \frac{(m+n)^2-2mn}{mn} \\ = \frac{(3)^2-2(4)}{4} \\ = \frac{9-8}{4} \\ = \frac{1}{4} [/tex]

Semoga membantu

Persamaan Kuadrat.

ax² + bx + c = 0
x² - 3x + 4 = 0

m + n = -b / a
mn = c / a
m - n = ±√D / a

[tex]\displaystyle \frac{m}{n}+\frac{n}{m}\\ =\frac{m^2+n^2}{mn}\\ =\frac{(m+n)^2-2mn}{mn}\\ =\frac{\left ( -\frac{-3}{1} \right )^2-2\left ( \frac{4}{1} \right )}{\frac{4}{1}}\\ =\frac{1}{4}[/tex]