9x+7/7x-9=4-0x/4x-7 eching

$$\frac{ 9x+7 }{ 7x-9 } = \frac{ 4-0x }{ 4x-7 }$$

x uchun yechish

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8}\approx 1,936478267$$

$$x=-\frac{\sqrt{649}}{24}+\frac{7}{8}\approx -0,186478267$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati \frac{9}{7},\frac{7}{4} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(4x-7\right)\left(7x-9\right) ga, 7x-9,4x-7 ning eng kichik karralisiga ko‘paytiring.

$$\left(4x-7\right)\left(9x+7\right)=\left(7x-9\right)\left(4-0x\right)$$

4x-7 ga 9x+7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0x\right)$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0\right)$$

4 olish uchun 4 dan 0 ni ayirish.

$$36x^{2}-35x-49=\left(7x-9\right)\times 4$$

7x-9 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36x^{2}-35x-49=28x-36$$

Ikkala tarafdan 28x ni ayirish.

$$36x^{2}-35x-49-28x=-36$$

-63x ni olish uchun -35x va -28x ni birlashtirish.

$$36x^{2}-63x-49=-36$$

36 ni ikki tarafga qo’shing.

$$36x^{2}-63x-49+36=0$$

-13 olish uchun -49 va 36'ni qo'shing.

$$36x^{2}-63x-13=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 36 ni a, -63 ni b va -13 ni c bilan almashtiring.

$$x=\frac{-\left(-63\right)±\sqrt{\left(-63\right)^{2}-4\times 36\left(-13\right)}}{2\times 36}$$

-63 kvadratini chiqarish.

$$x=\frac{-\left(-63\right)±\sqrt{3969-4\times 36\left(-13\right)}}{2\times 36}$$

-4 ni 36 marotabaga ko'paytirish.

$$x=\frac{-\left(-63\right)±\sqrt{3969-144\left(-13\right)}}{2\times 36}$$

-144 ni -13 marotabaga ko'paytirish.

$$x=\frac{-\left(-63\right)±\sqrt{3969+1872}}{2\times 36}$$

3969 ni 1872 ga qo'shish.

$$x=\frac{-\left(-63\right)±\sqrt{5841}}{2\times 36}$$

5841 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-63\right)±3\sqrt{649}}{2\times 36}$$

-63 ning teskarisi 63 ga teng.

$$x=\frac{63±3\sqrt{649}}{2\times 36}$$

2 ni 36 marotabaga ko'paytirish.

$$x=\frac{63±3\sqrt{649}}{72}$$

x=\frac{63±3\sqrt{649}}{72} tenglamasini yeching, bunda ± musbat. 63 ni 3\sqrt{649} ga qo'shish.

$$x=\frac{3\sqrt{649}+63}{72}$$

63+3\sqrt{649} ni 72 ga bo'lish.

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8}$$

x=\frac{63±3\sqrt{649}}{72} tenglamasini yeching, bunda ± manfiy. 63 dan 3\sqrt{649} ni ayirish.

$$x=\frac{63-3\sqrt{649}}{72}$$

63-3\sqrt{649} ni 72 ga bo'lish.

$$x=-\frac{\sqrt{649}}{24}+\frac{7}{8}$$

Tenglama yechildi.

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8} x=-\frac{\sqrt{649}}{24}+\frac{7}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati \frac{9}{7},\frac{7}{4} qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini \left(4x-7\right)\left(7x-9\right) ga, 7x-9,4x-7 ning eng kichik karralisiga ko‘paytiring.

$$\left(4x-7\right)\left(9x+7\right)=\left(7x-9\right)\left(4-0x\right)$$

4x-7 ga 9x+7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0x\right)$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$36x^{2}-35x-49=\left(7x-9\right)\left(4-0\right)$$

4 olish uchun 4 dan 0 ni ayirish.

$$36x^{2}-35x-49=\left(7x-9\right)\times 4$$

7x-9 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$36x^{2}-35x-49=28x-36$$

Ikkala tarafdan 28x ni ayirish.

$$36x^{2}-35x-49-28x=-36$$

-63x ni olish uchun -35x va -28x ni birlashtirish.

$$36x^{2}-63x-49=-36$$

49 ni ikki tarafga qo’shing.

$$36x^{2}-63x=-36+49$$

13 olish uchun -36 va 49'ni qo'shing.

$$36x^{2}-63x=13$$

Ikki tarafini 36 ga bo‘ling.

$$\frac{36x^{2}-63x}{36}=\frac{13}{36}$$

36 ga bo'lish 36 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{63}{36}\right)x=\frac{13}{36}$$

\frac{-63}{36} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{7}{4}x=\frac{13}{36}$$

-\frac{7}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{8} olish uchun. Keyin, -\frac{7}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{7}{4}x+\left(-\frac{7}{8}\right)^{2}=\frac{13}{36}+\left(-\frac{7}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{8} kvadratini chiqarish.

$$x^{2}-\frac{7}{4}x+\frac{49}{64}=\frac{13}{36}+\frac{49}{64}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{13}{36} ni \frac{49}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{7}{4}x+\frac{49}{64}=\frac{649}{576}$$

x^{2}-\frac{7}{4}x+\frac{49}{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.

$$\left(x-\frac{7}{8}\right)^{2}=\frac{649}{576}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{8}\right)^{2}}=\sqrt{\frac{649}{576}}$$

Qisqartirish.

$$x-\frac{7}{8}=\frac{\sqrt{649}}{24} x-\frac{7}{8}=-\frac{\sqrt{649}}{24}$$

\frac{7}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{649}}{24}+\frac{7}{8} x=-\frac{\sqrt{649}}{24}+\frac{7}{8}$$