5x-1/5x=6 eching

$$5 x - \frac { 1 } { 5 x } = 6$$

x uchun yechish

$$x=\frac{3-\sqrt{10}}{5}\approx -0,032455532$$

$$x = \frac{\sqrt{10} + 3}{5} \approx 1,232455532$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x ga ko'paytirish.

$$5x\times 5x-1=30x$$

25 hosil qilish uchun 5 va 5 ni ko'paytirish.

$$25xx-1=30x$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$25x^{2}-1=30x$$

Ikkala tarafdan 30x ni ayirish.

$$25x^{2}-1-30x=0$$

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.

$$25x^{2}-30x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 25 ni a, -30 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}-4\times 25\left(-1\right)}}{2\times 25}$$

-30 kvadratini chiqarish.

$$x=\frac{-\left(-30\right)±\sqrt{900-4\times 25\left(-1\right)}}{2\times 25}$$

-4 ni 25 marotabaga ko'paytirish.

$$x=\frac{-\left(-30\right)±\sqrt{900-100\left(-1\right)}}{2\times 25}$$

-100 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-30\right)±\sqrt{900+100}}{2\times 25}$$

900 ni 100 ga qo'shish.

$$x=\frac{-\left(-30\right)±\sqrt{1000}}{2\times 25}$$

1000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-30\right)±10\sqrt{10}}{2\times 25}$$

-30 ning teskarisi 30 ga teng.

$$x=\frac{30±10\sqrt{10}}{2\times 25}$$

2 ni 25 marotabaga ko'paytirish.

$$x=\frac{30±10\sqrt{10}}{50}$$

x=\frac{30±10\sqrt{10}}{50} tenglamasini yeching, bunda ± musbat. 30 ni 10\sqrt{10} ga qo'shish.

$$x=\frac{10\sqrt{10}+30}{50}$$

30+10\sqrt{10} ni 50 ga bo'lish.

$$x=\frac{\sqrt{10}+3}{5}$$

x=\frac{30±10\sqrt{10}}{50} tenglamasini yeching, bunda ± manfiy. 30 dan 10\sqrt{10} ni ayirish.

$$x=\frac{30-10\sqrt{10}}{50}$$

30-10\sqrt{10} ni 50 ga bo'lish.

$$x=\frac{3-\sqrt{10}}{5}$$

Tenglama yechildi.

$$x=\frac{\sqrt{10}+3}{5} x=\frac{3-\sqrt{10}}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x ga ko'paytirish.

$$5x\times 5x-1=30x$$

25 hosil qilish uchun 5 va 5 ni ko'paytirish.

$$25xx-1=30x$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$25x^{2}-1=30x$$

Ikkala tarafdan 30x ni ayirish.

$$25x^{2}-1-30x=0$$

1 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$25x^{2}-30x=1$$

Ikki tarafini 25 ga bo‘ling.

$$\frac{25x^{2}-30x}{25}=\frac{1}{25}$$

25 ga bo'lish 25 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{30}{25}\right)x=\frac{1}{25}$$

\frac{-30}{25} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{6}{5}x=\frac{1}{25}$$

-\frac{6}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{5} olish uchun. Keyin, -\frac{3}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{6}{5}x+\left(-\frac{3}{5}\right)^{2}=\frac{1}{25}+\left(-\frac{3}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{5} kvadratini chiqarish.

$$x^{2}-\frac{6}{5}x+\frac{9}{25}=\frac{1+9}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{25} ni \frac{9}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{6}{5}x+\frac{9}{25}=\frac{2}{5}$$

x^{2}-\frac{6}{5}x+\frac{9}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{5}\right)^{2}=\frac{2}{5}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{5}\right)^{2}}=\sqrt{\frac{2}{5}}$$

Qisqartirish.

$$x-\frac{3}{5}=\frac{\sqrt{10}}{5} x-\frac{3}{5}=-\frac{\sqrt{10}}{5}$$

\frac{3}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{10}+3}{5} x=\frac{3-\sqrt{10}}{5}$$