6/x^2-12/x=3 eching

$$\frac { 6 } { x ^ { 2 } } - \frac { 12 } { x } = 3$$

x uchun yechish (complex solution)

$$x=\sqrt{6}-2\approx 0,449489743$$

$$x=-\left(\sqrt{6}+2\right)\approx -4,449489743$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga, x^{2},x ning eng kichik karralisiga ko‘paytiring.

$$6-x\times 12=3x^{2}$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$6-x\times 12-3x^{2}=0$$

-12 hosil qilish uchun -1 va 12 ni ko'paytirish.

$$6-12x-3x^{2}=0$$

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.

$$-3x^{2}-12x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, -12 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-3\right)\times 6}}{2\left(-3\right)}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-3\right)\times 6}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+12\times 6}}{2\left(-3\right)}$$

12 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+72}}{2\left(-3\right)}$$

144 ni 72 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{216}}{2\left(-3\right)}$$

216 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±6\sqrt{6}}{2\left(-3\right)}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±6\sqrt{6}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{12±6\sqrt{6}}{-6}$$

x=\frac{12±6\sqrt{6}}{-6} tenglamasini yeching, bunda ± musbat. 12 ni 6\sqrt{6} ga qo'shish.

$$x=\frac{6\sqrt{6}+12}{-6}$$

12+6\sqrt{6} ni -6 ga bo'lish.

$$x=-\left(\sqrt{6}+2\right)$$

x=\frac{12±6\sqrt{6}}{-6} tenglamasini yeching, bunda ± manfiy. 12 dan 6\sqrt{6} ni ayirish.

$$x=\frac{12-6\sqrt{6}}{-6}$$

12-6\sqrt{6} ni -6 ga bo'lish.

$$x=\sqrt{6}-2$$

Tenglama yechildi.

$$x=-\left(\sqrt{6}+2\right) x=\sqrt{6}-2$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga, x^{2},x ning eng kichik karralisiga ko‘paytiring.

$$6-x\times 12=3x^{2}$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$6-x\times 12-3x^{2}=0$$

Ikkala tarafdan 6 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-x\times 12-3x^{2}=-6$$

-12 hosil qilish uchun -1 va 12 ni ko'paytirish.

$$-12x-3x^{2}=-6$$

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

$$-3x^{2}-12x=-6$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}-12x}{-3}=-\frac{6}{-3}$$

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

$$x^{2}+\left(-\frac{12}{-3}\right)x=-\frac{6}{-3}$$

-12 ni -3 ga bo'lish.

$$x^{2}+4x=-\frac{6}{-3}$$

-6 ni -3 ga bo'lish.

$$x^{2}+4x=2$$

4 ni bo‘lish, x shartining koeffitsienti, 2 ga 2 olish uchun. Keyin, 2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+4x+2^{2}=2+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=2+4$$

2 ni 4 ga qo'shish.

$$x^{2}+4x+4=6$$

x^{2}+4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+2\right)^{2}=6$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{6}$$

Qisqartirish.

$$x+2=\sqrt{6} x+2=-\sqrt{6}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=\sqrt{6}-2 x=-\sqrt{6}-2$$

x uchun yechish

$$x=\sqrt{6}-2\approx 0,449489743$$

$$x=-\sqrt{6}-2\approx -4,449489743$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga, x^{2},x ning eng kichik karralisiga ko‘paytiring.

$$6-x\times 12=3x^{2}$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$6-x\times 12-3x^{2}=0$$

-12 hosil qilish uchun -1 va 12 ni ko'paytirish.

$$6-12x-3x^{2}=0$$

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.

$$-3x^{2}-12x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, -12 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-3\right)\times 6}}{2\left(-3\right)}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-3\right)\times 6}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+12\times 6}}{2\left(-3\right)}$$

12 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+72}}{2\left(-3\right)}$$

144 ni 72 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{216}}{2\left(-3\right)}$$

216 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±6\sqrt{6}}{2\left(-3\right)}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±6\sqrt{6}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{12±6\sqrt{6}}{-6}$$

x=\frac{12±6\sqrt{6}}{-6} tenglamasini yeching, bunda ± musbat. 12 ni 6\sqrt{6} ga qo'shish.

$$x=\frac{6\sqrt{6}+12}{-6}$$

12+6\sqrt{6} ni -6 ga bo'lish.

$$x=-\left(\sqrt{6}+2\right)$$

x=\frac{12±6\sqrt{6}}{-6} tenglamasini yeching, bunda ± manfiy. 12 dan 6\sqrt{6} ni ayirish.

$$x=\frac{12-6\sqrt{6}}{-6}$$

12-6\sqrt{6} ni -6 ga bo'lish.

$$x=\sqrt{6}-2$$

Tenglama yechildi.

$$x=-\left(\sqrt{6}+2\right) x=\sqrt{6}-2$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x^{2} ga, x^{2},x ning eng kichik karralisiga ko‘paytiring.

$$6-x\times 12=3x^{2}$$

Ikkala tarafdan 3x^{2} ni ayirish.

$$6-x\times 12-3x^{2}=0$$

Ikkala tarafdan 6 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-x\times 12-3x^{2}=-6$$

-12 hosil qilish uchun -1 va 12 ni ko'paytirish.

$$-12x-3x^{2}=-6$$

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

$$-3x^{2}-12x=-6$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}-12x}{-3}=-\frac{6}{-3}$$

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

$$x^{2}+\left(-\frac{12}{-3}\right)x=-\frac{6}{-3}$$

-12 ni -3 ga bo'lish.

$$x^{2}+4x=-\frac{6}{-3}$$

-6 ni -3 ga bo'lish.

$$x^{2}+4x=2$$

4 ni bo‘lish, x shartining koeffitsienti, 2 ga 2 olish uchun. Keyin, 2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+4x+2^{2}=2+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=2+4$$

2 ni 4 ga qo'shish.

$$x^{2}+4x+4=6$$

x^{2}+4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+2\right)^{2}=6$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{6}$$

Qisqartirish.

$$x+2=\sqrt{6} x+2=-\sqrt{6}$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=\sqrt{6}-2 x=-\sqrt{6}-2$$