Himpunan Penyelesaian persamaan
[tex]3x ^{2} + 13 x - 10 = 0[/tex]
adalah.....
Note :
■ Menggunakan cara
■ No Copas!!!
■ No Asal
■ No Bahasa Alien
■ BA? Jawaban benar + Rapi + Menggunakan cara yang mudah dipahami
Jawab:
[tex]\large\boxed{Hp=\left[\frac{2}{3},~~-5\right]}[/tex]
Penjelasan dengan langkah-langkah:
[tex]3x^2+13x-10=0\\\\\frac{1}{3}(3x^2)+\frac{13x}{3}-\frac{10}{3}=0\\\\x^2+\frac{13x}{3}-\frac{10}{3}=0\\\\\because x^2+bx+c=0\\\rightarrow x^2+bx+(\frac{1}{2}\cdot b)^2=(\frac{1}{2}\cdot b)^2-c\\\\\therefore x^2+\frac{13x}{3}-\frac{10}{3}=0\\\\\rightarrow x^2+\frac{13x}{3}+(\frac{1}{2}\cdot \frac{13}{3})^2=(\frac{1}{2}\cdot \frac{13}{3})^2+\frac{10}{3}\\\\x^2+\frac{13x}{3}+(\frac{13}{6})^2=(\frac{13}{6})^2+\frac{10}{3}\\\\x^2+\frac{(2)13x}{2(3)}+(\frac{13}{6})^2=\frac{13^2}{6^2}+\frac{10\cdot12}{3\cdot12}[/tex]
[tex]x^2+\frac{26x}{6}+(\frac{13}{6})^2=\frac{169}{36}+\frac{120}{36}\\\\x^2+2x(\frac{13}{6})+(\frac{13}{6})^2=\frac{289}{36}\\\\(~~a=x,~~b=\frac{13}{6}~~)\\\\\because a^2+2ab+b^2=(a+b)^2\therefore\\\\(x+\frac{13}{6})^2=\frac{289}{36}\\\\x+\frac{13}{6}=\pm\sqrt{\frac{289}{36}}\\\\x+\frac{13}{6}=\pm\frac{\sqrt{289}}{\sqrt{36}}\\\\x+\frac{13}{6}=\pm\frac{17}{6}\\\\x=\pm\frac{17}{6}-\frac{13}{6}[/tex]
[tex]\sf Hp=\left[\frac{17}{6}-\frac{13}{6},~~-\frac{17}{6}-\frac{13}{6}\right]\\\\Hp=\left[\frac{17-13}{6},~~\frac{-17-13}{6}\right]\\\\Hp=\left[\frac{4}{6},~~\frac{-30}{6}\right]\\\\Hp=\left[\frac{4\div2}{6\div2},~~-\frac{30}{6}\right]\\\\\large\boxed{Hp=\left[\frac{2}{3},~~-5\right]}[/tex]
(Xcvi)
[answer.2.content]
