243h^2+17h=-10 eching

$$243 h ^ { 2 } + 17 h = - 10$$

h uchun yechish

$$h=\frac{-17+\sqrt{9431}i}{486}\approx -0,034979424+0,199821679i$$

$$h=\frac{-\sqrt{9431}i-17}{486}\approx -0,034979424-0,199821679i$$

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.

$$243h^{2}+17h=-10$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$243h^{2}+17h-\left(-10\right)=-10-\left(-10\right)$$

O‘zidan -10 ayirilsa 0 qoladi.

$$243h^{2}+17h-\left(-10\right)=0$$

0 dan -10 ni ayirish.

$$243h^{2}+17h+10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 243 ni a, 17 ni b va 10 ni c bilan almashtiring.

$$h=\frac{-17±\sqrt{17^{2}-4\times 243\times 10}}{2\times 243}$$

17 kvadratini chiqarish.

$$h=\frac{-17±\sqrt{289-4\times 243\times 10}}{2\times 243}$$

-4 ni 243 marotabaga ko'paytirish.

$$h=\frac{-17±\sqrt{289-972\times 10}}{2\times 243}$$

-972 ni 10 marotabaga ko'paytirish.

$$h=\frac{-17±\sqrt{289-9720}}{2\times 243}$$

289 ni -9720 ga qo'shish.

$$h=\frac{-17±\sqrt{-9431}}{2\times 243}$$

-9431 ning kvadrat ildizini chiqarish.

$$h=\frac{-17±\sqrt{9431}i}{2\times 243}$$

2 ni 243 marotabaga ko'paytirish.

$$h=\frac{-17±\sqrt{9431}i}{486}$$

h=\frac{-17±\sqrt{9431}i}{486} tenglamasini yeching, bunda ± musbat. -17 ni i\sqrt{9431} ga qo'shish.

$$h=\frac{-17+\sqrt{9431}i}{486}$$

h=\frac{-17±\sqrt{9431}i}{486} tenglamasini yeching, bunda ± manfiy. -17 dan i\sqrt{9431} ni ayirish.

$$h=\frac{-\sqrt{9431}i-17}{486}$$

Tenglama yechildi.

$$h=\frac{-17+\sqrt{9431}i}{486} h=\frac{-\sqrt{9431}i-17}{486}$$

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.

$$243h^{2}+17h=-10$$

Ikki tarafini 243 ga bo‘ling.

$$\frac{243h^{2}+17h}{243}=-\frac{10}{243}$$

243 ga bo'lish 243 ga ko'paytirishni bekor qiladi.

$$h^{2}+\frac{17}{243}h=-\frac{10}{243}$$

\frac{17}{243} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{17}{486} olish uchun. Keyin, \frac{17}{486} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$h^{2}+\frac{17}{243}h+\left(\frac{17}{486}\right)^{2}=-\frac{10}{243}+\left(\frac{17}{486}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{17}{486} kvadratini chiqarish.

$$h^{2}+\frac{17}{243}h+\frac{289}{236196}=-\frac{10}{243}+\frac{289}{236196}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{10}{243} ni \frac{289}{236196} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$h^{2}+\frac{17}{243}h+\frac{289}{236196}=-\frac{9431}{236196}$$

h^{2}+\frac{17}{243}h+\frac{289}{236196} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(h+\frac{17}{486}\right)^{2}=-\frac{9431}{236196}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(h+\frac{17}{486}\right)^{2}}=\sqrt{-\frac{9431}{236196}}$$

Qisqartirish.

$$h+\frac{17}{486}=\frac{\sqrt{9431}i}{486} h+\frac{17}{486}=-\frac{\sqrt{9431}i}{486}$$

Tenglamaning ikkala tarafidan \frac{17}{486} ni ayirish.

$$h=\frac{-17+\sqrt{9431}i}{486} h=\frac{-\sqrt{9431}i-17}{486}$$