6v^2+5v-3=0 eching

$$6 v ^ { 2 } + 5 v - 3 = 0$$

v uchun yechish

$$v=\frac{\sqrt{97}-5}{12}\approx 0,404071483$$

$$v=\frac{-\sqrt{97}-5}{12}\approx -1,237404817$$

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.

$$6v^{2}+5v-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 5 ni b va -3 ni c bilan almashtiring.

$$v=\frac{-5±\sqrt{5^{2}-4\times 6\left(-3\right)}}{2\times 6}$$

5 kvadratini chiqarish.

$$v=\frac{-5±\sqrt{25-4\times 6\left(-3\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$v=\frac{-5±\sqrt{25-24\left(-3\right)}}{2\times 6}$$

-24 ni -3 marotabaga ko'paytirish.

$$v=\frac{-5±\sqrt{25+72}}{2\times 6}$$

25 ni 72 ga qo'shish.

$$v=\frac{-5±\sqrt{97}}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$v=\frac{-5±\sqrt{97}}{12}$$

v=\frac{-5±\sqrt{97}}{12} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{97} ga qo'shish.

$$v=\frac{\sqrt{97}-5}{12}$$

v=\frac{-5±\sqrt{97}}{12} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{97} ni ayirish.

$$v=\frac{-\sqrt{97}-5}{12}$$

Tenglama yechildi.

$$v=\frac{\sqrt{97}-5}{12} v=\frac{-\sqrt{97}-5}{12}$$

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.

$$6v^{2}+5v-3=0$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$6v^{2}+5v-3-\left(-3\right)=-\left(-3\right)$$

O‘zidan -3 ayirilsa 0 qoladi.

$$6v^{2}+5v=-\left(-3\right)$$

0 dan -3 ni ayirish.

$$6v^{2}+5v=3$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6v^{2}+5v}{6}=\frac{3}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$v^{2}+\frac{5}{6}v=\frac{3}{6}$$

\frac{3}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$v^{2}+\frac{5}{6}v=\frac{1}{2}$$

\frac{5}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{12} olish uchun. Keyin, \frac{5}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$v^{2}+\frac{5}{6}v+\left(\frac{5}{12}\right)^{2}=\frac{1}{2}+\left(\frac{5}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{12} kvadratini chiqarish.

$$v^{2}+\frac{5}{6}v+\frac{25}{144}=\frac{1}{2}+\frac{25}{144}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2} ni \frac{25}{144} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$v^{2}+\frac{5}{6}v+\frac{25}{144}=\frac{97}{144}$$

v^{2}+\frac{5}{6}v+\frac{25}{144} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(v+\frac{5}{12}\right)^{2}=\frac{97}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(v+\frac{5}{12}\right)^{2}}=\sqrt{\frac{97}{144}}$$

Qisqartirish.

$$v+\frac{5}{12}=\frac{\sqrt{97}}{12} v+\frac{5}{12}=-\frac{\sqrt{97}}{12}$$

Tenglamaning ikkala tarafidan \frac{5}{12} ni ayirish.

$$v=\frac{\sqrt{97}-5}{12} v=\frac{-\sqrt{97}-5}{12}$$