x/x-3+x=7x-14/x-3 eching

$$\frac { x } { x - 3 } + x = \frac { 7 x - 14 } { x - 3 }$$

x uchun yechish

$$x=2$$

$$x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-3 ga ko'paytirish.

$$x+\left(x-3\right)x=7x-14$$

x-3 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x+x^{2}-3x=7x-14$$

-2x ni olish uchun x va -3x ni birlashtirish.

$$-2x+x^{2}=7x-14$$

Ikkala tarafdan 7x ni ayirish.

$$-2x+x^{2}-7x=-14$$

-9x ni olish uchun -2x va -7x ni birlashtirish.

$$-9x+x^{2}=-14$$

14 ni ikki tarafga qo’shing.

$$-9x+x^{2}+14=0$$

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.

$$x^{2}-9x+14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -9 ni b va 14 ni c bilan almashtiring.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 14}}{2}$$

-9 kvadratini chiqarish.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 14}}{2}$$

-4 ni 14 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81-56}}{2}$$

81 ni -56 ga qo'shish.

$$x=\frac{-\left(-9\right)±\sqrt{25}}{2}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±5}{2}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±5}{2}$$

x=\frac{9±5}{2} tenglamasini yeching, bunda ± musbat. 9 ni 5 ga qo'shish.

$$x=\frac{14}{2}$$

14 ni 2 ga bo'lish.

$$x=7$$

x=\frac{9±5}{2} tenglamasini yeching, bunda ± manfiy. 9 dan 5 ni ayirish.

$$x=\frac{4}{2}$$

4 ni 2 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=7 x=2$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 3 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-3 ga ko'paytirish.

$$x+\left(x-3\right)x=7x-14$$

x-3 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x+x^{2}-3x=7x-14$$

-2x ni olish uchun x va -3x ni birlashtirish.

$$-2x+x^{2}=7x-14$$

Ikkala tarafdan 7x ni ayirish.

$$-2x+x^{2}-7x=-14$$

-9x ni olish uchun -2x va -7x ni birlashtirish.

$$-9x+x^{2}=-14$$

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

$$x^{2}-9x=-14$$

-9 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{2} olish uchun. Keyin, -\frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=-14+\left(-\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.

$$x^{2}-9x+\frac{81}{4}=-14+\frac{81}{4}$$

-14 ni \frac{81}{4} ga qo'shish.

$$x^{2}-9x+\frac{81}{4}=\frac{25}{4}$$

x^{2}-9x+\frac{81}{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.

$$\left(x-\frac{9}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

$$x-\frac{9}{2}=\frac{5}{2} x-\frac{9}{2}=-\frac{5}{2}$$

\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=2$$