10/9x^2-12/10x=0 eching

$$\frac { 10 } { 9 } x ^ { 2 } - \frac { 12 } { 10 } x = 0$$

x uchun yechish

$$x = \frac{27}{25} = 1\frac{2}{25} = 1,08$$

$$x=0$$

Faktorlash qadamlari

\frac{12}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{10}{9}x^{2}-\frac{6}{5}x=0$$

x omili.

$$x\left(\frac{10}{9}x-\frac{6}{5}\right)=0$$

Tenglamani yechish uchun x=0 va \frac{10x}{9}-\frac{6}{5}=0 ni yeching.

$$x=0 x=\frac{27}{25}$$

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.

$$\frac{10}{9}x^{2}-\frac{6}{5}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{10}{9} ni a, -\frac{6}{5} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{6}{5}\right)±\sqrt{\left(-\frac{6}{5}\right)^{2}}}{2\times \frac{10}{9}}$$

\left(-\frac{6}{5}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{6}{5}\right)±\frac{6}{5}}{2\times \frac{10}{9}}$$

-\frac{6}{5} ning teskarisi \frac{6}{5} ga teng.

$$x=\frac{\frac{6}{5}±\frac{6}{5}}{2\times \frac{10}{9}}$$

2 ni \frac{10}{9} marotabaga ko'paytirish.

$$x=\frac{\frac{6}{5}±\frac{6}{5}}{\frac{20}{9}}$$

x=\frac{\frac{6}{5}±\frac{6}{5}}{\frac{20}{9}} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{6}{5} ni \frac{6}{5} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{\frac{12}{5}}{\frac{20}{9}}$$

\frac{12}{5} ni \frac{20}{9} ga bo'lish \frac{12}{5} ga k'paytirish \frac{20}{9} ga qaytarish.

$$x=\frac{27}{25}$$

x=\frac{\frac{6}{5}±\frac{6}{5}}{\frac{20}{9}} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{6}{5} ni \frac{6}{5} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=\frac{0}{\frac{20}{9}}$$

0 ni \frac{20}{9} ga bo'lish 0 ga k'paytirish \frac{20}{9} ga qaytarish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{27}{25} x=0$$

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.

$$\frac{10}{9}x^{2}-\frac{6}{5}x=0$$

Tenglamaning ikki tarafini \frac{10}{9} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{\frac{10}{9}x^{2}-\frac{6}{5}x}{\frac{10}{9}}=\frac{0}{\frac{10}{9}}$$

\frac{10}{9} ga bo'lish \frac{10}{9} ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{\frac{6}{5}}{\frac{10}{9}}\right)x=\frac{0}{\frac{10}{9}}$$

-\frac{6}{5} ni \frac{10}{9} ga bo'lish -\frac{6}{5} ga k'paytirish \frac{10}{9} ga qaytarish.

$$x^{2}-\frac{27}{25}x=\frac{0}{\frac{10}{9}}$$

0 ni \frac{10}{9} ga bo'lish 0 ga k'paytirish \frac{10}{9} ga qaytarish.

$$x^{2}-\frac{27}{25}x=0$$

-\frac{27}{25} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{27}{50} olish uchun. Keyin, -\frac{27}{50} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{27}{25}x+\left(-\frac{27}{50}\right)^{2}=\left(-\frac{27}{50}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{27}{50} kvadratini chiqarish.

$$x^{2}-\frac{27}{25}x+\frac{729}{2500}=\frac{729}{2500}$$

x^{2}-\frac{27}{25}x+\frac{729}{2500} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{27}{50}\right)^{2}=\frac{729}{2500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{27}{50}\right)^{2}}=\sqrt{\frac{729}{2500}}$$

Qisqartirish.

$$x-\frac{27}{50}=\frac{27}{50} x-\frac{27}{50}=-\frac{27}{50}$$

\frac{27}{50} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{27}{25} x=0$$