x uchun yechish
x=\frac{\sqrt{10}-1}{3}\approx 0,72075922
x=\frac{-\sqrt{10}-1}{3}\approx -1,387425887
Grafik
Baham ko'rish
Klipbordga nusxa olish
3x^{2}+2x-3=0
ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.
x=\frac{-2±\sqrt{2^{2}-4\times 3\left(-3\right)}}{2\times 3}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 2 ni b va -3 ni c bilan almashtiring.
x=\frac{-2±\sqrt{4-4\times 3\left(-3\right)}}{2\times 3}
2 kvadratini chiqarish.
x=\frac{-2±\sqrt{4-12\left(-3\right)}}{2\times 3}
-4 ni 3 marotabaga ko'paytirish.
x=\frac{-2±\sqrt{4+36}}{2\times 3}
-12 ni -3 marotabaga ko'paytirish.
x=\frac{-2±\sqrt{40}}{2\times 3}
4 ni 36 ga qo'shish.
x=\frac{-2±2\sqrt{10}}{2\times 3}
40 ning kvadrat ildizini chiqarish.
x=\frac{-2±2\sqrt{10}}{6}
2 ni 3 marotabaga ko'paytirish.
x=\frac{2\sqrt{10}-2}{6}
x=\frac{-2±2\sqrt{10}}{6} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{10} ga qo'shish.
x=\frac{\sqrt{10}-1}{3}
-2+2\sqrt{10} ni 6 ga bo'lish.
x=\frac{-2\sqrt{10}-2}{6}
x=\frac{-2±2\sqrt{10}}{6} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{10} ni ayirish.
x=\frac{-\sqrt{10}-1}{3}
-2-2\sqrt{10} ni 6 ga bo'lish.
x=\frac{\sqrt{10}-1}{3} x=\frac{-\sqrt{10}-1}{3}
Tenglama yechildi.
3x^{2}+2x-3=0
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
3x^{2}+2x-3-\left(-3\right)=-\left(-3\right)
3 ni tenglamaning ikkala tarafiga qo'shish.
3x^{2}+2x=-\left(-3\right)
O‘zidan -3 ayirilsa 0 qoladi.
3x^{2}+2x=3
0 dan -3 ni ayirish.
\frac{3x^{2}+2x}{3}=\frac{3}{3}
Ikki tarafini 3 ga bo‘ling.
x^{2}+\frac{2}{3}x=\frac{3}{3}
3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.
x^{2}+\frac{2}{3}x=1
3 ni 3 ga bo'lish.
x^{2}+\frac{2}{3}x+\left(\frac{1}{3}\right)^{2}=1+\left(\frac{1}{3}\right)^{2}
\frac{2}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{3} olish uchun. Keyin, \frac{1}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}+\frac{2}{3}x+\frac{1}{9}=1+\frac{1}{9}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{3} kvadratini chiqarish.
x^{2}+\frac{2}{3}x+\frac{1}{9}=\frac{10}{9}
1 ni \frac{1}{9} ga qo'shish.
\left(x+\frac{1}{3}\right)^{2}=\frac{10}{9}
x^{2}+\frac{2}{3}x+\frac{1}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(x+\frac{1}{3}\right)^{2}}=\sqrt{\frac{10}{9}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+\frac{1}{3}=\frac{\sqrt{10}}{3} x+\frac{1}{3}=-\frac{\sqrt{10}}{3}
Qisqartirish.
x=\frac{\sqrt{10}-1}{3} x=\frac{-\sqrt{10}-1}{3}
Tenglamaning ikkala tarafidan \frac{1}{3} ni ayirish.
Misollar
Ikkilik tenglama
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometriya
4 \sin \theta \cos \theta = 2 \sin \theta
Chiziqli tenglama
y = 3x + 4
Arifmetik
699 * 533
Matritsa
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simli tenglama
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differensatsiya
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Oʻngga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Chegaralar
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}