Qz 25/ ∞akar akar persamaan kuadrat [tex]3x {}^{2} + 2x - 5 = 0 \: \: adalah \: \\ x1 \: \: dan \: x.... Question from @Ghost03

JΟY

${\sf{\dfrac{1}{x_1}+\dfrac{1}{x_2}}}={\boldsymbol{\dfrac{\textsf{\textbf{2}}}{\textsf{\textbf{5}}}}}$

Penjelasan dengan langkah-langkah :

#Cara pertama

$\begin{aligned}&{\sf{\text{-}~Nilai~x_1~dan~x_2}}\\&~~{\sf{3x^2+2x-5=0}}\\&~~{\sf{(3x+5)(x-1)=0}}\\&\begin{array}{c|c}{\sf{3x+5=0}}&{\sf{x-1=0}}\\{\sf{3x=0-5}}&{\sf{x=0+1}}\\{\sf{3x=-5\quad}}&{\sf{x_2=1\qquad}}\\{\sf{x_1=-\dfrac{5}{3}~~~}}&\end{array}\\\\&{\sf{\text{-}~Hasil~dari~\frac{1}{x_1}+\frac{1}{x_2}}}\\&~~{\sf{=\frac{1}{x_1}+\frac{1}{x_2}}}\\&~~{\sf{=-\frac{1}{\frac{5}{3}}+\frac{1}{1}}}\\&~~{\sf{=-\left(1\cdot\frac{3}{5}\right)+\frac{1}{1}}}\\&~~{\sf{=-\frac{3}{5}+\frac{1}{1}}}\\&~~{\sf{=-\frac{3}{5}+\frac{5}{5}}}\\&~~{\sf{=\frac{-3+5}{5}}}\\&~~{\sf{=\frac{2}{5}}}\end{aligned}$

$>#Cara kedua<img src=$

8 votes Thanks 9

Gusti2601

$\mathbb \color{aqua} \underbrace{JAWABAN}$

$\implies \small \boxed{ \bold{ \frac{2}{5} }}$

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$\mathbb \color{orange} \underbrace{PENYELESAIAN}$

=> menentukan nilai x :

$\sf x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac}}{2a}$

$\sf x = \frac{ - 2 ± \sqrt{ {2}^{2} - 4(3)( - 5)} }{2(3)}$

$\sf x = \frac{ - 2 ± \sqrt{4 + 60} }{6}$

$\sf x = \frac{ - 2 ± \sqrt{64} }{6}$

$\sf x = \frac{ - 2 ± 8}{6}$

$\\$

maka :

$\sf x_1 = \frac{ - 2 + 8}{6}$

$\sf x_1 = \frac{6}{6}$

$\sf x_1 =1$

$\\$

$\sf x_2 = \frac{ - 2 - 8}{6}$

$\sf x_2 = \frac{ - 10}{6}$

$\sf x_2 = - \frac{10}{6}$

$\sf x_2 = - \frac{5}{3}$

$\\$

${\small{\textsf{\textbf{=>}}}} { \underline{ \bold{hasil \: dari \: \frac{1}{x_1} + \frac{1}{x_2}}} : }$

$\sf \longrightarrow \frac{1}{x_1} + \frac{1}{x_2}$

$\sf \longrightarrow \frac{1}{1} + \frac{1}{ - \frac{5}{3} }$

$\sf \longrightarrow \frac{1}{1} + ( - \frac{3}{5} )$

$\sf \longrightarrow \frac{1}{1} - \frac{3}{5}$

$\sf \longrightarrow \frac{5}{5} - \frac{3}{5}$

$\sf \longrightarrow \frac{5 - 3}{5}$

$\sf \longrightarrow \bold{ \frac{2}{5} }$

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$\mathbb \color{red} \underbrace{KESIMPULAN}$

$\sf Jadi, hasil \: dari \: \bold{ \frac{1}{x_1} + \frac{1}{x_2}} \: adalah \: \bold{ \frac{2}{5} }$

$\colorbox{ff0000}{} \colorbox{ff4000}{}\colorbox{ff8000}{}\colorbox{ffc000}{}\colorbox{ffff00}{}\colorbox{c0ff00}{}\colorbox{80ff00}{}\colorbox{40ff00}{}\colorbox{00ff00}{}\colorbox{00ff40}{}\colorbox{00ff80}{}\colorbox{00ffc0}{}\colorbox{00ffff}{}\colorbox{00c0ff}{}\colorbox{0080ff}{}\colorbox{0040ff}{}\colorbox{0000ff}{}\colorbox{4000ff}{}\colorbox{8000ff}{}\colorbox{c000ff}{}\colorbox{ff00ff}{}\colorbox{ff00c0}{}\colorbox{ff00a0}{}\colorbox{ff0080}{}\colorbox{ff0040}{}$

1 votes Thanks 5

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