x^2-5x+3=1/4x+1 eching

$$x ^ { 2 } - 5 x + 3 = \frac { 1 } { 4 } x + 1$$

x uchun yechish

$$x = \frac{\sqrt{313} + 21}{8} \approx 4,836475752$$

$$x=\frac{21-\sqrt{313}}{8}\approx 0,413524248$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{1}{4}x ni ayirish.

$$x^{2}-5x+3-\frac{1}{4}x=1$$

-\frac{21}{4}x ni olish uchun -5x va -\frac{1}{4}x ni birlashtirish.

$$x^{2}-\frac{21}{4}x+3=1$$

Ikkala tarafdan 1 ni ayirish.

$$x^{2}-\frac{21}{4}x+3-1=0$$

2 olish uchun 3 dan 1 ni ayirish.

$$x^{2}-\frac{21}{4}x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -\frac{21}{4} ni b va 2 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{21}{4}\right)±\sqrt{\left(-\frac{21}{4}\right)^{2}-4\times 2}}{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{21}{4} kvadratini chiqarish.

$$x=\frac{-\left(-\frac{21}{4}\right)±\sqrt{\frac{441}{16}-4\times 2}}{2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{21}{4}\right)±\sqrt{\frac{441}{16}-8}}{2}$$

\frac{441}{16} ni -8 ga qo'shish.

$$x=\frac{-\left(-\frac{21}{4}\right)±\sqrt{\frac{313}{16}}}{2}$$

\frac{313}{16} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{21}{4}\right)±\frac{\sqrt{313}}{4}}{2}$$

-\frac{21}{4} ning teskarisi \frac{21}{4} ga teng.

$$x=\frac{\frac{21}{4}±\frac{\sqrt{313}}{4}}{2}$$

x=\frac{\frac{21}{4}±\frac{\sqrt{313}}{4}}{2} tenglamasini yeching, bunda ± musbat. \frac{21}{4} ni \frac{\sqrt{313}}{4} ga qo'shish.

$$x=\frac{\sqrt{313}+21}{2\times 4}$$

\frac{21+\sqrt{313}}{4} ni 2 ga bo'lish.

$$x=\frac{\sqrt{313}+21}{8}$$

x=\frac{\frac{21}{4}±\frac{\sqrt{313}}{4}}{2} tenglamasini yeching, bunda ± manfiy. \frac{21}{4} dan \frac{\sqrt{313}}{4} ni ayirish.

$$x=\frac{21-\sqrt{313}}{2\times 4}$$

\frac{21-\sqrt{313}}{4} ni 2 ga bo'lish.

$$x=\frac{21-\sqrt{313}}{8}$$

Tenglama yechildi.

$$x=\frac{\sqrt{313}+21}{8} x=\frac{21-\sqrt{313}}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan \frac{1}{4}x ni ayirish.

$$x^{2}-5x+3-\frac{1}{4}x=1$$

-\frac{21}{4}x ni olish uchun -5x va -\frac{1}{4}x ni birlashtirish.

$$x^{2}-\frac{21}{4}x+3=1$$

Ikkala tarafdan 3 ni ayirish.

$$x^{2}-\frac{21}{4}x=1-3$$

-2 olish uchun 1 dan 3 ni ayirish.

$$x^{2}-\frac{21}{4}x=-2$$

-\frac{21}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{21}{8} olish uchun. Keyin, -\frac{21}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{21}{4}x+\left(-\frac{21}{8}\right)^{2}=-2+\left(-\frac{21}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{21}{8} kvadratini chiqarish.

$$x^{2}-\frac{21}{4}x+\frac{441}{64}=-2+\frac{441}{64}$$

-2 ni \frac{441}{64} ga qo'shish.

$$x^{2}-\frac{21}{4}x+\frac{441}{64}=\frac{313}{64}$$

x^{2}-\frac{21}{4}x+\frac{441}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{21}{8}\right)^{2}=\frac{313}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{21}{8}\right)^{2}}=\sqrt{\frac{313}{64}}$$

Qisqartirish.

$$x-\frac{21}{8}=\frac{\sqrt{313}}{8} x-\frac{21}{8}=-\frac{\sqrt{313}}{8}$$

\frac{21}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{313}+21}{8} x=\frac{21-\sqrt{313}}{8}$$