9x+7/7x-9=9-8x/4x-7 eching

$$\frac { 9 x + 7 } { 7 x - 9 } = \frac { 9 - 8 x } { 4 x - 7 }$$

x uchun yechish

$$x = \frac{\sqrt{4281} + 85}{92} \approx 1,635101644$$

$$x=\frac{85-\sqrt{4281}}{92}\approx 0,212724443$$

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.

$$\left(4x-7\right)\left(9x+7\right)=\left(7x-9\right)\left(9-8x\right)$$

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

$$36x^{2}-35x-49=\left(7x-9\right)\left(9-8x\right)$$

7x-9 ga 9-8x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36x^{2}-35x-49=135x-56x^{2}-81$$

Ikkala tarafdan 135x ni ayirish.

$$36x^{2}-35x-49-135x=-56x^{2}-81$$

-170x ni olish uchun -35x va -135x ni birlashtirish.

$$36x^{2}-170x-49=-56x^{2}-81$$

56x^{2} ni ikki tarafga qo’shing.

$$36x^{2}-170x-49+56x^{2}=-81$$

92x^{2} ni olish uchun 36x^{2} va 56x^{2} ni birlashtirish.

$$92x^{2}-170x-49=-81$$

81 ni ikki tarafga qo’shing.

$$92x^{2}-170x-49+81=0$$

32 olish uchun -49 va 81'ni qo'shing.

$$92x^{2}-170x+32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 92 ni a, -170 ni b va 32 ni c bilan almashtiring.

$$x=\frac{-\left(-170\right)±\sqrt{\left(-170\right)^{2}-4\times 92\times 32}}{2\times 92}$$

-170 kvadratini chiqarish.

$$x=\frac{-\left(-170\right)±\sqrt{28900-4\times 92\times 32}}{2\times 92}$$

-4 ni 92 marotabaga ko'paytirish.

$$x=\frac{-\left(-170\right)±\sqrt{28900-368\times 32}}{2\times 92}$$

-368 ni 32 marotabaga ko'paytirish.

$$x=\frac{-\left(-170\right)±\sqrt{28900-11776}}{2\times 92}$$

28900 ni -11776 ga qo'shish.

$$x=\frac{-\left(-170\right)±\sqrt{17124}}{2\times 92}$$

17124 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-170\right)±2\sqrt{4281}}{2\times 92}$$

-170 ning teskarisi 170 ga teng.

$$x=\frac{170±2\sqrt{4281}}{2\times 92}$$

2 ni 92 marotabaga ko'paytirish.

$$x=\frac{170±2\sqrt{4281}}{184}$$

x=\frac{170±2\sqrt{4281}}{184} tenglamasini yeching, bunda ± musbat. 170 ni 2\sqrt{4281} ga qo'shish.

$$x=\frac{2\sqrt{4281}+170}{184}$$

170+2\sqrt{4281} ni 184 ga bo'lish.

$$x=\frac{\sqrt{4281}+85}{92}$$

x=\frac{170±2\sqrt{4281}}{184} tenglamasini yeching, bunda ± manfiy. 170 dan 2\sqrt{4281} ni ayirish.

$$x=\frac{170-2\sqrt{4281}}{184}$$

170-2\sqrt{4281} ni 184 ga bo'lish.

$$x=\frac{85-\sqrt{4281}}{92}$$

Tenglama yechildi.

$$x=\frac{\sqrt{4281}+85}{92} x=\frac{85-\sqrt{4281}}{92}$$

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.

$$\left(4x-7\right)\left(9x+7\right)=\left(7x-9\right)\left(9-8x\right)$$

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

$$36x^{2}-35x-49=\left(7x-9\right)\left(9-8x\right)$$

7x-9 ga 9-8x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36x^{2}-35x-49=135x-56x^{2}-81$$

Ikkala tarafdan 135x ni ayirish.

$$36x^{2}-35x-49-135x=-56x^{2}-81$$

-170x ni olish uchun -35x va -135x ni birlashtirish.

$$36x^{2}-170x-49=-56x^{2}-81$$

56x^{2} ni ikki tarafga qo’shing.

$$36x^{2}-170x-49+56x^{2}=-81$$

92x^{2} ni olish uchun 36x^{2} va 56x^{2} ni birlashtirish.

$$92x^{2}-170x-49=-81$$

49 ni ikki tarafga qo’shing.

$$92x^{2}-170x=-81+49$$

-32 olish uchun -81 va 49'ni qo'shing.

$$92x^{2}-170x=-32$$

Ikki tarafini 92 ga bo‘ling.

$$\frac{92x^{2}-170x}{92}=-\frac{32}{92}$$

92 ga bo'lish 92 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{170}{92}\right)x=-\frac{32}{92}$$

\frac{-170}{92} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{85}{46}x=-\frac{32}{92}$$

\frac{-32}{92} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{85}{46}x=-\frac{8}{23}$$

-\frac{85}{46} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{85}{92} olish uchun. Keyin, -\frac{85}{92} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{85}{46}x+\left(-\frac{85}{92}\right)^{2}=-\frac{8}{23}+\left(-\frac{85}{92}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{85}{92} kvadratini chiqarish.

$$x^{2}-\frac{85}{46}x+\frac{7225}{8464}=-\frac{8}{23}+\frac{7225}{8464}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{8}{23} ni \frac{7225}{8464} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{85}{46}x+\frac{7225}{8464}=\frac{4281}{8464}$$

x^{2}-\frac{85}{46}x+\frac{7225}{8464} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{85}{92}\right)^{2}=\frac{4281}{8464}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{85}{92}\right)^{2}}=\sqrt{\frac{4281}{8464}}$$

Qisqartirish.

$$x-\frac{85}{92}=\frac{\sqrt{4281}}{92} x-\frac{85}{92}=-\frac{\sqrt{4281}}{92}$$

\frac{85}{92} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{4281}+85}{92} x=\frac{85-\sqrt{4281}}{92}$$