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

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

x uchun yechish

$$x = \frac{\sqrt{15305} + 163}{176} \approx 1,629053286$$

$$x=\frac{163-\sqrt{15305}}{176}\approx 0,223219441$$

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.

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

4x-7 ga 8x+7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$32x^{2}-28x-49=\left(7x-9\right)\left(9-8x\right)$$

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

$$32x^{2}-28x-49=135x-56x^{2}-81$$

Ikkala tarafdan 135x ni ayirish.

$$32x^{2}-28x-49-135x=-56x^{2}-81$$

-163x ni olish uchun -28x va -135x ni birlashtirish.

$$32x^{2}-163x-49=-56x^{2}-81$$

56x^{2} ni ikki tarafga qo’shing.

$$32x^{2}-163x-49+56x^{2}=-81$$

88x^{2} ni olish uchun 32x^{2} va 56x^{2} ni birlashtirish.

$$88x^{2}-163x-49=-81$$

81 ni ikki tarafga qo’shing.

$$88x^{2}-163x-49+81=0$$

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

$$88x^{2}-163x+32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 88 ni a, -163 ni b va 32 ni c bilan almashtiring.

$$x=\frac{-\left(-163\right)±\sqrt{\left(-163\right)^{2}-4\times 88\times 32}}{2\times 88}$$

-163 kvadratini chiqarish.

$$x=\frac{-\left(-163\right)±\sqrt{26569-4\times 88\times 32}}{2\times 88}$$

-4 ni 88 marotabaga ko'paytirish.

$$x=\frac{-\left(-163\right)±\sqrt{26569-352\times 32}}{2\times 88}$$

-352 ni 32 marotabaga ko'paytirish.

$$x=\frac{-\left(-163\right)±\sqrt{26569-11264}}{2\times 88}$$

26569 ni -11264 ga qo'shish.

$$x=\frac{-\left(-163\right)±\sqrt{15305}}{2\times 88}$$

-163 ning teskarisi 163 ga teng.

$$x=\frac{163±\sqrt{15305}}{2\times 88}$$

2 ni 88 marotabaga ko'paytirish.

$$x=\frac{163±\sqrt{15305}}{176}$$

x=\frac{163±\sqrt{15305}}{176} tenglamasini yeching, bunda ± musbat. 163 ni \sqrt{15305} ga qo'shish.

$$x=\frac{\sqrt{15305}+163}{176}$$

x=\frac{163±\sqrt{15305}}{176} tenglamasini yeching, bunda ± manfiy. 163 dan \sqrt{15305} ni ayirish.

$$x=\frac{163-\sqrt{15305}}{176}$$

Tenglama yechildi.

$$x=\frac{\sqrt{15305}+163}{176} x=\frac{163-\sqrt{15305}}{176}$$

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.

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

4x-7 ga 8x+7 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$32x^{2}-28x-49=\left(7x-9\right)\left(9-8x\right)$$

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

$$32x^{2}-28x-49=135x-56x^{2}-81$$

Ikkala tarafdan 135x ni ayirish.

$$32x^{2}-28x-49-135x=-56x^{2}-81$$

-163x ni olish uchun -28x va -135x ni birlashtirish.

$$32x^{2}-163x-49=-56x^{2}-81$$

56x^{2} ni ikki tarafga qo’shing.

$$32x^{2}-163x-49+56x^{2}=-81$$

88x^{2} ni olish uchun 32x^{2} va 56x^{2} ni birlashtirish.

$$88x^{2}-163x-49=-81$$

49 ni ikki tarafga qo’shing.

$$88x^{2}-163x=-81+49$$

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

$$88x^{2}-163x=-32$$

Ikki tarafini 88 ga bo‘ling.

$$\frac{88x^{2}-163x}{88}=-\frac{32}{88}$$

88 ga bo'lish 88 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{163}{88}x=-\frac{32}{88}$$

\frac{-32}{88} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{163}{88}x=-\frac{4}{11}$$

-\frac{163}{88} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{163}{176} olish uchun. Keyin, -\frac{163}{176} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{163}{88}x+\left(-\frac{163}{176}\right)^{2}=-\frac{4}{11}+\left(-\frac{163}{176}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{163}{176} kvadratini chiqarish.

$$x^{2}-\frac{163}{88}x+\frac{26569}{30976}=-\frac{4}{11}+\frac{26569}{30976}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{4}{11} ni \frac{26569}{30976} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{163}{88}x+\frac{26569}{30976}=\frac{15305}{30976}$$

x^{2}-\frac{163}{88}x+\frac{26569}{30976} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{163}{176}\right)^{2}=\frac{15305}{30976}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{163}{176}\right)^{2}}=\sqrt{\frac{15305}{30976}}$$

Qisqartirish.

$$x-\frac{163}{176}=\frac{\sqrt{15305}}{176} x-\frac{163}{176}=-\frac{\sqrt{15305}}{176}$$

\frac{163}{176} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{15305}+163}{176} x=\frac{163-\sqrt{15305}}{176}$$