34x^2-24x-1/(x+1)(x-1)=0 eching

$$\frac { 34 x ^ { 2 } - 24 x - 1 } { ( x + 1 ) ( x - 1 ) } = 0$$

x uchun yechish

$$x=\frac{\sqrt{178}}{34}+\frac{6}{17}\approx 0,745343061$$

$$x=-\frac{\sqrt{178}}{34}+\frac{6}{17}\approx -0,039460708$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+1\right) ga ko'paytirish.

$$34x^{2}-24x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 34 ni a, -24 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 34\left(-1\right)}}{2\times 34}$$

-24 kvadratini chiqarish.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 34\left(-1\right)}}{2\times 34}$$

-4 ni 34 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576-136\left(-1\right)}}{2\times 34}$$

-136 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576+136}}{2\times 34}$$

576 ni 136 ga qo'shish.

$$x=\frac{-\left(-24\right)±\sqrt{712}}{2\times 34}$$

712 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-24\right)±2\sqrt{178}}{2\times 34}$$

-24 ning teskarisi 24 ga teng.

$$x=\frac{24±2\sqrt{178}}{2\times 34}$$

2 ni 34 marotabaga ko'paytirish.

$$x=\frac{24±2\sqrt{178}}{68}$$

x=\frac{24±2\sqrt{178}}{68} tenglamasini yeching, bunda ± musbat. 24 ni 2\sqrt{178} ga qo'shish.

$$x=\frac{2\sqrt{178}+24}{68}$$

24+2\sqrt{178} ni 68 ga bo'lish.

$$x=\frac{\sqrt{178}}{34}+\frac{6}{17}$$

x=\frac{24±2\sqrt{178}}{68} tenglamasini yeching, bunda ± manfiy. 24 dan 2\sqrt{178} ni ayirish.

$$x=\frac{24-2\sqrt{178}}{68}$$

24-2\sqrt{178} ni 68 ga bo'lish.

$$x=-\frac{\sqrt{178}}{34}+\frac{6}{17}$$

Tenglama yechildi.

$$x=\frac{\sqrt{178}}{34}+\frac{6}{17} x=-\frac{\sqrt{178}}{34}+\frac{6}{17}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -1,1 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(x-1\right)\left(x+1\right) ga ko'paytirish.

$$34x^{2}-24x-1=0$$

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$34x^{2}-24x=1$$

Ikki tarafini 34 ga bo‘ling.

$$\frac{34x^{2}-24x}{34}=\frac{1}{34}$$

34 ga bo'lish 34 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{24}{34}\right)x=\frac{1}{34}$$

\frac{-24}{34} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{12}{17}x=\frac{1}{34}$$

-\frac{12}{17} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{6}{17} olish uchun. Keyin, -\frac{6}{17} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{12}{17}x+\left(-\frac{6}{17}\right)^{2}=\frac{1}{34}+\left(-\frac{6}{17}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{6}{17} kvadratini chiqarish.

$$x^{2}-\frac{12}{17}x+\frac{36}{289}=\frac{1}{34}+\frac{36}{289}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{34} ni \frac{36}{289} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{12}{17}x+\frac{36}{289}=\frac{89}{578}$$

x^{2}-\frac{12}{17}x+\frac{36}{289} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{6}{17}\right)^{2}=\frac{89}{578}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{6}{17}\right)^{2}}=\sqrt{\frac{89}{578}}$$

Qisqartirish.

$$x-\frac{6}{17}=\frac{\sqrt{178}}{34} x-\frac{6}{17}=-\frac{\sqrt{178}}{34}$$

\frac{6}{17} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{178}}{34}+\frac{6}{17} x=-\frac{\sqrt{178}}{34}+\frac{6}{17}$$