35r^2-72r+36=0 eching

$$35 r ^ { 2 } - 72 r + 36 = 0$$

r uchun yechish

$$r=\frac{6}{7}\approx 0,857142857$$

$$r = \frac{6}{5} = 1\frac{1}{5} = 1,2$$

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.

$$35r^{2}-72r+36=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 35 ni a, -72 ni b va 36 ni c bilan almashtiring.

$$r=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 35\times 36}}{2\times 35}$$

-72 kvadratini chiqarish.

$$r=\frac{-\left(-72\right)±\sqrt{5184-4\times 35\times 36}}{2\times 35}$$

-4 ni 35 marotabaga ko'paytirish.

$$r=\frac{-\left(-72\right)±\sqrt{5184-140\times 36}}{2\times 35}$$

-140 ni 36 marotabaga ko'paytirish.

$$r=\frac{-\left(-72\right)±\sqrt{5184-5040}}{2\times 35}$$

5184 ni -5040 ga qo'shish.

$$r=\frac{-\left(-72\right)±\sqrt{144}}{2\times 35}$$

144 ning kvadrat ildizini chiqarish.

$$r=\frac{-\left(-72\right)±12}{2\times 35}$$

-72 ning teskarisi 72 ga teng.

$$r=\frac{72±12}{2\times 35}$$

2 ni 35 marotabaga ko'paytirish.

$$r=\frac{72±12}{70}$$

r=\frac{72±12}{70} tenglamasini yeching, bunda ± musbat. 72 ni 12 ga qo'shish.

$$r=\frac{84}{70}$$

\frac{84}{70} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$r=\frac{6}{5}$$

r=\frac{72±12}{70} tenglamasini yeching, bunda ± manfiy. 72 dan 12 ni ayirish.

$$r=\frac{60}{70}$$

\frac{60}{70} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$r=\frac{6}{7}$$

Tenglama yechildi.

$$r=\frac{6}{5} r=\frac{6}{7}$$

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.

$$35r^{2}-72r+36=0$$

Tenglamaning ikkala tarafidan 36 ni ayirish.

$$35r^{2}-72r+36-36=-36$$

O‘zidan 36 ayirilsa 0 qoladi.

$$35r^{2}-72r=-36$$

Ikki tarafini 35 ga bo‘ling.

$$\frac{35r^{2}-72r}{35}=-\frac{36}{35}$$

35 ga bo'lish 35 ga ko'paytirishni bekor qiladi.

$$r^{2}-\frac{72}{35}r=-\frac{36}{35}$$

-\frac{72}{35} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{36}{35} olish uchun. Keyin, -\frac{36}{35} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$r^{2}-\frac{72}{35}r+\left(-\frac{36}{35}\right)^{2}=-\frac{36}{35}+\left(-\frac{36}{35}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{36}{35} kvadratini chiqarish.

$$r^{2}-\frac{72}{35}r+\frac{1296}{1225}=-\frac{36}{35}+\frac{1296}{1225}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{36}{35} ni \frac{1296}{1225} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$r^{2}-\frac{72}{35}r+\frac{1296}{1225}=\frac{36}{1225}$$

r^{2}-\frac{72}{35}r+\frac{1296}{1225} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(r-\frac{36}{35}\right)^{2}=\frac{36}{1225}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(r-\frac{36}{35}\right)^{2}}=\sqrt{\frac{36}{1225}}$$

Qisqartirish.

$$r-\frac{36}{35}=\frac{6}{35} r-\frac{36}{35}=-\frac{6}{35}$$

\frac{36}{35} ni tenglamaning ikkala tarafiga qo'shish.

$$r=\frac{6}{5} r=\frac{6}{7}$$