4:2/x-4/5=3/x eching

$$4 : \frac { 2 } { x } - \frac { 4 } { 5 } = \frac { 3 } { x }$$

x uchun yechish

$$x=-\frac{\sqrt{154}}{10}+\frac{1}{5}\approx -1,040967365$$

$$x=\frac{\sqrt{154}}{10}+\frac{1}{5}\approx 1,440967365$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x ga, 5,x ning eng kichik karralisiga ko‘paytiring.

$$\frac{5}{2}x^{2}\times 4+5x\left(-\frac{4}{5}\right)=5\times 3$$

10 hosil qilish uchun \frac{5}{2} va 4 ni ko'paytirish.

$$10x^{2}+5x\left(-\frac{4}{5}\right)=5\times 3$$

-4 hosil qilish uchun 5 va -\frac{4}{5} ni ko'paytirish.

$$10x^{2}-4x=5\times 3$$

15 hosil qilish uchun 5 va 3 ni ko'paytirish.

$$10x^{2}-4x=15$$

Ikkala tarafdan 15 ni ayirish.

$$10x^{2}-4x-15=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 10 ni a, -4 ni b va -15 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 10\left(-15\right)}}{2\times 10}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 10\left(-15\right)}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-40\left(-15\right)}}{2\times 10}$$

-40 ni -15 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+600}}{2\times 10}$$

16 ni 600 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{616}}{2\times 10}$$

616 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{154}}{2\times 10}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{154}}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$x=\frac{4±2\sqrt{154}}{20}$$

x=\frac{4±2\sqrt{154}}{20} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{154} ga qo'shish.

$$x=\frac{2\sqrt{154}+4}{20}$$

4+2\sqrt{154} ni 20 ga bo'lish.

$$x=\frac{\sqrt{154}}{10}+\frac{1}{5}$$

x=\frac{4±2\sqrt{154}}{20} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{154} ni ayirish.

$$x=\frac{4-2\sqrt{154}}{20}$$

4-2\sqrt{154} ni 20 ga bo'lish.

$$x=-\frac{\sqrt{154}}{10}+\frac{1}{5}$$

Tenglama yechildi.

$$x=\frac{\sqrt{154}}{10}+\frac{1}{5} x=-\frac{\sqrt{154}}{10}+\frac{1}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x ga, 5,x ning eng kichik karralisiga ko‘paytiring.

$$\frac{5}{2}x^{2}\times 4+5x\left(-\frac{4}{5}\right)=5\times 3$$

10 hosil qilish uchun \frac{5}{2} va 4 ni ko'paytirish.

$$10x^{2}+5x\left(-\frac{4}{5}\right)=5\times 3$$

-4 hosil qilish uchun 5 va -\frac{4}{5} ni ko'paytirish.

$$10x^{2}-4x=5\times 3$$

15 hosil qilish uchun 5 va 3 ni ko'paytirish.

$$10x^{2}-4x=15$$

Ikki tarafini 10 ga bo‘ling.

$$\frac{10x^{2}-4x}{10}=\frac{15}{10}$$

10 ga bo'lish 10 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{4}{10}\right)x=\frac{15}{10}$$

\frac{-4}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{2}{5}x=\frac{15}{10}$$

\frac{15}{10} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{2}{5}x=\frac{3}{2}$$

-\frac{2}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{5} olish uchun. Keyin, -\frac{1}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{5} kvadratini chiqarish.

$$x^{2}-\frac{2}{5}x+\frac{1}{25}=\frac{3}{2}+\frac{1}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni \frac{1}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{2}{5}x+\frac{1}{25}=\frac{77}{50}$$

x^{2}-\frac{2}{5}x+\frac{1}{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.

$$\left(x-\frac{1}{5}\right)^{2}=\frac{77}{50}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{5}\right)^{2}}=\sqrt{\frac{77}{50}}$$

Qisqartirish.

$$x-\frac{1}{5}=\frac{\sqrt{154}}{10} x-\frac{1}{5}=-\frac{\sqrt{154}}{10}$$

\frac{1}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{154}}{10}+\frac{1}{5} x=-\frac{\sqrt{154}}{10}+\frac{1}{5}$$