12/p-24=3p-13/p-24-3/p eching

$$\frac { 12 } { p - 24 } = \frac { 3 p - 13 } { p - 24 } - \frac { 3 } { p }$$

p uchun yechish

$$p=\frac{14+2\sqrt{5}i}{3}\approx 4,666666667+1,490711985i$$

$$p=\frac{-2\sqrt{5}i+14}{3}\approx 4,666666667-1,490711985i$$

Kvadrat tenglamalaridan foydalanish qoidalari

p qiymati 0,24 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini p\left(p-24\right) ga, p-24,p ning eng kichik karralisiga ko‘paytiring.

$$p\times 12=p\left(3p-13\right)-\left(p-24\right)\times 3$$

p ga 3p-13 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$p\times 12=3p^{2}-13p-\left(p-24\right)\times 3$$

p-24 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$p\times 12=3p^{2}-13p-\left(3p-72\right)$$

3p-72 teskarisini topish uchun har birining teskarisini toping.

$$p\times 12=3p^{2}-13p-3p+72$$

-16p ni olish uchun -13p va -3p ni birlashtirish.

$$p\times 12=3p^{2}-16p+72$$

Ikkala tarafdan 3p^{2} ni ayirish.

$$p\times 12-3p^{2}=-16p+72$$

16p ni ikki tarafga qo’shing.

$$p\times 12-3p^{2}+16p=72$$

28p ni olish uchun p\times 12 va 16p ni birlashtirish.

$$28p-3p^{2}=72$$

Ikkala tarafdan 72 ni ayirish.

$$28p-3p^{2}-72=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-3p^{2}+28p-72=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 28 ni b va -72 ni c bilan almashtiring.

$$p=\frac{-28±\sqrt{28^{2}-4\left(-3\right)\left(-72\right)}}{2\left(-3\right)}$$

28 kvadratini chiqarish.

$$p=\frac{-28±\sqrt{784-4\left(-3\right)\left(-72\right)}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$p=\frac{-28±\sqrt{784+12\left(-72\right)}}{2\left(-3\right)}$$

12 ni -72 marotabaga ko'paytirish.

$$p=\frac{-28±\sqrt{784-864}}{2\left(-3\right)}$$

784 ni -864 ga qo'shish.

$$p=\frac{-28±\sqrt{-80}}{2\left(-3\right)}$$

-80 ning kvadrat ildizini chiqarish.

$$p=\frac{-28±4\sqrt{5}i}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$p=\frac{-28±4\sqrt{5}i}{-6}$$

p=\frac{-28±4\sqrt{5}i}{-6} tenglamasini yeching, bunda ± musbat. -28 ni 4i\sqrt{5} ga qo'shish.

$$p=\frac{-28+4\sqrt{5}i}{-6}$$

-28+4i\sqrt{5} ni -6 ga bo'lish.

$$p=\frac{-2\sqrt{5}i+14}{3}$$

p=\frac{-28±4\sqrt{5}i}{-6} tenglamasini yeching, bunda ± manfiy. -28 dan 4i\sqrt{5} ni ayirish.

$$p=\frac{-4\sqrt{5}i-28}{-6}$$

-28-4i\sqrt{5} ni -6 ga bo'lish.

$$p=\frac{14+2\sqrt{5}i}{3}$$

Tenglama yechildi.

$$p=\frac{-2\sqrt{5}i+14}{3} p=\frac{14+2\sqrt{5}i}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

p qiymati 0,24 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini p\left(p-24\right) ga, p-24,p ning eng kichik karralisiga ko‘paytiring.

$$p\times 12=p\left(3p-13\right)-\left(p-24\right)\times 3$$

p ga 3p-13 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$p\times 12=3p^{2}-13p-\left(p-24\right)\times 3$$

p-24 ga 3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$p\times 12=3p^{2}-13p-\left(3p-72\right)$$

3p-72 teskarisini topish uchun har birining teskarisini toping.

$$p\times 12=3p^{2}-13p-3p+72$$

-16p ni olish uchun -13p va -3p ni birlashtirish.

$$p\times 12=3p^{2}-16p+72$$

Ikkala tarafdan 3p^{2} ni ayirish.

$$p\times 12-3p^{2}=-16p+72$$

16p ni ikki tarafga qo’shing.

$$p\times 12-3p^{2}+16p=72$$

28p ni olish uchun p\times 12 va 16p ni birlashtirish.

$$28p-3p^{2}=72$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-3p^{2}+28p=72$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3p^{2}+28p}{-3}=\frac{72}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$p^{2}+\frac{28}{-3}p=\frac{72}{-3}$$

28 ni -3 ga bo'lish.

$$p^{2}-\frac{28}{3}p=\frac{72}{-3}$$

72 ni -3 ga bo'lish.

$$p^{2}-\frac{28}{3}p=-24$$

-\frac{28}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{14}{3} olish uchun. Keyin, -\frac{14}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$p^{2}-\frac{28}{3}p+\left(-\frac{14}{3}\right)^{2}=-24+\left(-\frac{14}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{14}{3} kvadratini chiqarish.

$$p^{2}-\frac{28}{3}p+\frac{196}{9}=-24+\frac{196}{9}$$

-24 ni \frac{196}{9} ga qo'shish.

$$p^{2}-\frac{28}{3}p+\frac{196}{9}=-\frac{20}{9}$$

p^{2}-\frac{28}{3}p+\frac{196}{9} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(p-\frac{14}{3}\right)^{2}=-\frac{20}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(p-\frac{14}{3}\right)^{2}}=\sqrt{-\frac{20}{9}}$$

Qisqartirish.

$$p-\frac{14}{3}=\frac{2\sqrt{5}i}{3} p-\frac{14}{3}=-\frac{2\sqrt{5}i}{3}$$

\frac{14}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$p=\frac{14+2\sqrt{5}i}{3} p=\frac{-2\sqrt{5}i+14}{3}$$