86t^2-76t+17=0 eching

$$86 t ^ { 2 } - 76 t + 17 = 0$$

t uchun yechish

$$t=\frac{3\sqrt{2}i}{86}+\frac{19}{43}\approx 0,441860465+0,049333031i$$

$$t=-\frac{3\sqrt{2}i}{86}+\frac{19}{43}\approx 0,441860465-0,049333031i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$86t^{2}-76t+17=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 86 ni a, -76 ni b va 17 ni c bilan almashtiring.

$$t=\frac{-\left(-76\right)±\sqrt{\left(-76\right)^{2}-4\times 86\times 17}}{2\times 86}$$

-76 kvadratini chiqarish.

$$t=\frac{-\left(-76\right)±\sqrt{5776-4\times 86\times 17}}{2\times 86}$$

-4 ni 86 marotabaga ko'paytirish.

$$t=\frac{-\left(-76\right)±\sqrt{5776-344\times 17}}{2\times 86}$$

-344 ni 17 marotabaga ko'paytirish.

$$t=\frac{-\left(-76\right)±\sqrt{5776-5848}}{2\times 86}$$

5776 ni -5848 ga qo'shish.

$$t=\frac{-\left(-76\right)±\sqrt{-72}}{2\times 86}$$

-72 ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-76\right)±6\sqrt{2}i}{2\times 86}$$

-76 ning teskarisi 76 ga teng.

$$t=\frac{76±6\sqrt{2}i}{2\times 86}$$

2 ni 86 marotabaga ko'paytirish.

$$t=\frac{76±6\sqrt{2}i}{172}$$

t=\frac{76±6\sqrt{2}i}{172} tenglamasini yeching, bunda ± musbat. 76 ni 6i\sqrt{2} ga qo'shish.

$$t=\frac{76+6\sqrt{2}i}{172}$$

76+6i\sqrt{2} ni 172 ga bo'lish.

$$t=\frac{3\sqrt{2}i}{86}+\frac{19}{43}$$

t=\frac{76±6\sqrt{2}i}{172} tenglamasini yeching, bunda ± manfiy. 76 dan 6i\sqrt{2} ni ayirish.

$$t=\frac{-6\sqrt{2}i+76}{172}$$

76-6i\sqrt{2} ni 172 ga bo'lish.

$$t=-\frac{3\sqrt{2}i}{86}+\frac{19}{43}$$

Tenglama yechildi.

$$t=\frac{3\sqrt{2}i}{86}+\frac{19}{43} t=-\frac{3\sqrt{2}i}{86}+\frac{19}{43}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$86t^{2}-76t+17=0$$

Tenglamaning ikkala tarafidan 17 ni ayirish.

$$86t^{2}-76t+17-17=-17$$

O‘zidan 17 ayirilsa 0 qoladi.

$$86t^{2}-76t=-17$$

Ikki tarafini 86 ga bo‘ling.

$$\frac{86t^{2}-76t}{86}=-\frac{17}{86}$$

86 ga bo'lish 86 ga ko'paytirishni bekor qiladi.

$$t^{2}+\left(-\frac{76}{86}\right)t=-\frac{17}{86}$$

\frac{-76}{86} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$t^{2}-\frac{38}{43}t=-\frac{17}{86}$$

-\frac{38}{43} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{19}{43} olish uchun. Keyin, -\frac{19}{43} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-\frac{38}{43}t+\left(-\frac{19}{43}\right)^{2}=-\frac{17}{86}+\left(-\frac{19}{43}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{19}{43} kvadratini chiqarish.

$$t^{2}-\frac{38}{43}t+\frac{361}{1849}=-\frac{17}{86}+\frac{361}{1849}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{17}{86} ni \frac{361}{1849} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$t^{2}-\frac{38}{43}t+\frac{361}{1849}=-\frac{9}{3698}$$

t^{2}-\frac{38}{43}t+\frac{361}{1849} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-\frac{19}{43}\right)^{2}=-\frac{9}{3698}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-\frac{19}{43}\right)^{2}}=\sqrt{-\frac{9}{3698}}$$

Qisqartirish.

$$t-\frac{19}{43}=\frac{3\sqrt{2}i}{86} t-\frac{19}{43}=-\frac{3\sqrt{2}i}{86}$$

\frac{19}{43} ni tenglamaning ikkala tarafiga qo'shish.

$$t=\frac{3\sqrt{2}i}{86}+\frac{19}{43} t=-\frac{3\sqrt{2}i}{86}+\frac{19}{43}$$