x uchun yechish
x=\sqrt{3}+2\approx 3,732050808
x=2-\sqrt{3}\approx 0,267949192
Grafik
Baham ko'rish
Klipbordga nusxa olish
x^{2}+1-4x=0
Ikkala tarafdan 4x ni ayirish.
x^{2}-4x+1=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{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4 ni b va 1 ni c bilan almashtiring.
x=\frac{-\left(-4\right)±\sqrt{16-4}}{2}
-4 kvadratini chiqarish.
x=\frac{-\left(-4\right)±\sqrt{12}}{2}
16 ni -4 ga qo'shish.
x=\frac{-\left(-4\right)±2\sqrt{3}}{2}
12 ning kvadrat ildizini chiqarish.
x=\frac{4±2\sqrt{3}}{2}
-4 ning teskarisi 4 ga teng.
x=\frac{2\sqrt{3}+4}{2}
x=\frac{4±2\sqrt{3}}{2} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{3} ga qo'shish.
x=\sqrt{3}+2
4+2\sqrt{3} ni 2 ga bo'lish.
x=\frac{4-2\sqrt{3}}{2}
x=\frac{4±2\sqrt{3}}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{3} ni ayirish.
x=2-\sqrt{3}
4-2\sqrt{3} ni 2 ga bo'lish.
x=\sqrt{3}+2 x=2-\sqrt{3}
Tenglama yechildi.
x^{2}+1-4x=0
Ikkala tarafdan 4x ni ayirish.
x^{2}-4x=-1
Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.
x^{2}-4x+\left(-2\right)^{2}=-1+\left(-2\right)^{2}
-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}-4x+4=-1+4
-2 kvadratini chiqarish.
x^{2}-4x+4=3
-1 ni 4 ga qo'shish.
\left(x-2\right)^{2}=3
x^{2}-4x+4 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-2\right)^{2}}=\sqrt{3}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-2=\sqrt{3} x-2=-\sqrt{3}
Qisqartirish.
x=\sqrt{3}+2 x=2-\sqrt{3}
2 ni tenglamaning ikkala tarafiga qo'shish.
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}