21/x+1=16/x-2-6/x eching

$$\frac { 21 } { x + 1 } = \frac { 16 } { x - 2 } - \frac { 6 } { x }$$

x uchun yechish

$$x=-\frac{2}{11}\approx -0,181818182$$

$$x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -1,0,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-2\right)\left(x+1\right) ga, x+1,x-2,x ning eng kichik karralisiga ko‘paytiring.

$$x\left(x-2\right)\times 21=x\left(x+1\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x^{2}-2x\right)\times 21=x\left(x+1\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x^{2}-2x ga 21 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=x\left(x+1\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=\left(x^{2}+x\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x^{2}+x ga 16 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=16x^{2}+16x-\left(x-2\right)\left(x+1\right)\times 6$$

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$21x^{2}-42x=16x^{2}+16x-\left(x^{2}-x-2\right)\times 6$$

x^{2}-x-2 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=16x^{2}+16x-\left(6x^{2}-6x-12\right)$$

6x^{2}-6x-12 teskarisini topish uchun har birining teskarisini toping.

$$21x^{2}-42x=16x^{2}+16x-6x^{2}+6x+12$$

10x^{2} ni olish uchun 16x^{2} va -6x^{2} ni birlashtirish.

$$21x^{2}-42x=10x^{2}+16x+6x+12$$

22x ni olish uchun 16x va 6x ni birlashtirish.

$$21x^{2}-42x=10x^{2}+22x+12$$

Ikkala tarafdan 10x^{2} ni ayirish.

$$21x^{2}-42x-10x^{2}=22x+12$$

11x^{2} ni olish uchun 21x^{2} va -10x^{2} ni birlashtirish.

$$11x^{2}-42x=22x+12$$

Ikkala tarafdan 22x ni ayirish.

$$11x^{2}-42x-22x=12$$

-64x ni olish uchun -42x va -22x ni birlashtirish.

$$11x^{2}-64x=12$$

Ikkala tarafdan 12 ni ayirish.

$$11x^{2}-64x-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 11 ni a, -64 ni b va -12 ni c bilan almashtiring.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 11\left(-12\right)}}{2\times 11}$$

-64 kvadratini chiqarish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4\times 11\left(-12\right)}}{2\times 11}$$

-4 ni 11 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-44\left(-12\right)}}{2\times 11}$$

-44 ni -12 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096+528}}{2\times 11}$$

4096 ni 528 ga qo'shish.

$$x=\frac{-\left(-64\right)±\sqrt{4624}}{2\times 11}$$

4624 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-64\right)±68}{2\times 11}$$

-64 ning teskarisi 64 ga teng.

$$x=\frac{64±68}{2\times 11}$$

2 ni 11 marotabaga ko'paytirish.

$$x=\frac{64±68}{22}$$

x=\frac{64±68}{22} tenglamasini yeching, bunda ± musbat. 64 ni 68 ga qo'shish.

$$x=\frac{132}{22}$$

132 ni 22 ga bo'lish.

$$x=6$$

x=\frac{64±68}{22} tenglamasini yeching, bunda ± manfiy. 64 dan 68 ni ayirish.

$$x=-\frac{4}{22}$$

\frac{-4}{22} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{2}{11}$$

Tenglama yechildi.

$$x=6 x=-\frac{2}{11}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -1,0,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-2\right)\left(x+1\right) ga, x+1,x-2,x ning eng kichik karralisiga ko‘paytiring.

$$x\left(x-2\right)\times 21=x\left(x+1\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x^{2}-2x\right)\times 21=x\left(x+1\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x^{2}-2x ga 21 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=x\left(x+1\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=\left(x^{2}+x\right)\times 16-\left(x-2\right)\left(x+1\right)\times 6$$

x^{2}+x ga 16 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=16x^{2}+16x-\left(x-2\right)\left(x+1\right)\times 6$$

x-2 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$21x^{2}-42x=16x^{2}+16x-\left(x^{2}-x-2\right)\times 6$$

x^{2}-x-2 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$21x^{2}-42x=16x^{2}+16x-\left(6x^{2}-6x-12\right)$$

6x^{2}-6x-12 teskarisini topish uchun har birining teskarisini toping.

$$21x^{2}-42x=16x^{2}+16x-6x^{2}+6x+12$$

10x^{2} ni olish uchun 16x^{2} va -6x^{2} ni birlashtirish.

$$21x^{2}-42x=10x^{2}+16x+6x+12$$

22x ni olish uchun 16x va 6x ni birlashtirish.

$$21x^{2}-42x=10x^{2}+22x+12$$

Ikkala tarafdan 10x^{2} ni ayirish.

$$21x^{2}-42x-10x^{2}=22x+12$$

11x^{2} ni olish uchun 21x^{2} va -10x^{2} ni birlashtirish.

$$11x^{2}-42x=22x+12$$

Ikkala tarafdan 22x ni ayirish.

$$11x^{2}-42x-22x=12$$

-64x ni olish uchun -42x va -22x ni birlashtirish.

$$11x^{2}-64x=12$$

Ikki tarafini 11 ga bo‘ling.

$$\frac{11x^{2}-64x}{11}=\frac{12}{11}$$

11 ga bo'lish 11 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{64}{11}x=\frac{12}{11}$$

-\frac{64}{11} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{32}{11} olish uchun. Keyin, -\frac{32}{11} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{64}{11}x+\left(-\frac{32}{11}\right)^{2}=\frac{12}{11}+\left(-\frac{32}{11}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{32}{11} kvadratini chiqarish.

$$x^{2}-\frac{64}{11}x+\frac{1024}{121}=\frac{12}{11}+\frac{1024}{121}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{12}{11} ni \frac{1024}{121} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{64}{11}x+\frac{1024}{121}=\frac{1156}{121}$$

x^{2}-\frac{64}{11}x+\frac{1024}{121} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{32}{11}\right)^{2}=\frac{1156}{121}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{32}{11}\right)^{2}}=\sqrt{\frac{1156}{121}}$$

Qisqartirish.

$$x-\frac{32}{11}=\frac{34}{11} x-\frac{32}{11}=-\frac{34}{11}$$

\frac{32}{11} ni tenglamaning ikkala tarafiga qo'shish.

$$x=6 x=-\frac{2}{11}$$