24x^2-72x+48=0 eching

$$24 x ^ { 2 } - 72 x + 48 = 0$$

x uchun yechish

$$x=1$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$24x^{2}-72x+48=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 24 ni a, -72 ni b va 48 ni c bilan almashtiring.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 24\times 48}}{2\times 24}$$

-72 kvadratini chiqarish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4\times 24\times 48}}{2\times 24}$$

-4 ni 24 marotabaga ko'paytirish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-96\times 48}}{2\times 24}$$

-96 ni 48 marotabaga ko'paytirish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4608}}{2\times 24}$$

5184 ni -4608 ga qo'shish.

$$x=\frac{-\left(-72\right)±\sqrt{576}}{2\times 24}$$

576 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-72\right)±24}{2\times 24}$$

-72 ning teskarisi 72 ga teng.

$$x=\frac{72±24}{2\times 24}$$

2 ni 24 marotabaga ko'paytirish.

$$x=\frac{72±24}{48}$$

x=\frac{72±24}{48} tenglamasini yeching, bunda ± musbat. 72 ni 24 ga qo'shish.

$$x=\frac{96}{48}$$

96 ni 48 ga bo'lish.

$$x=2$$

x=\frac{72±24}{48} tenglamasini yeching, bunda ± manfiy. 72 dan 24 ni ayirish.

$$x=\frac{48}{48}$$

48 ni 48 ga bo'lish.

$$x=1$$

Tenglama yechildi.

$$x=2 x=1$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$24x^{2}-72x+48=0$$

Tenglamaning ikkala tarafidan 48 ni ayirish.

$$24x^{2}-72x+48-48=-48$$

O‘zidan 48 ayirilsa 0 qoladi.

$$24x^{2}-72x=-48$$

Ikki tarafini 24 ga bo‘ling.

$$\frac{24x^{2}-72x}{24}=-\frac{48}{24}$$

24 ga bo'lish 24 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{72}{24}\right)x=-\frac{48}{24}$$

-72 ni 24 ga bo'lish.

$$x^{2}-3x=-\frac{48}{24}$$

-48 ni 24 ga bo'lish.

$$x^{2}-3x=-2$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=-2+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=-2+\frac{9}{4}$$

-2 ni \frac{9}{4} ga qo'shish.

$$x^{2}-3x+\frac{9}{4}=\frac{1}{4}$$

x^{2}-3x+\frac{9}{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.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{1}{2} x-\frac{3}{2}=-\frac{1}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=2 x=1$$