2x/1x-x/2+x+1/4=6x eching

$$\frac { 2 x } { 1 } x - \frac { x } { 2 } + \frac { x + 1 } { 4 } = 6 x$$

x uchun yechish

$$x = \frac{\sqrt{593} + 25}{16} \approx 3,084474458$$

$$x=\frac{25-\sqrt{593}}{16}\approx 0,040525542$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 4 ga, 2,4 ning eng kichik karralisiga ko‘paytiring.

$$4\times 2xx-2x+x+1=24x$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$8xx-2x+x+1=24x$$

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

$$8x^{2}-2x+x+1=24x$$

-x ni olish uchun -2x va x ni birlashtirish.

$$8x^{2}-x+1=24x$$

Ikkala tarafdan 24x ni ayirish.

$$8x^{2}-x+1-24x=0$$

-25x ni olish uchun -x va -24x ni birlashtirish.

$$8x^{2}-25x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, -25 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}-4\times 8}}{2\times 8}$$

-25 kvadratini chiqarish.

$$x=\frac{-\left(-25\right)±\sqrt{625-4\times 8}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-\left(-25\right)±\sqrt{625-32}}{2\times 8}$$

625 ni -32 ga qo'shish.

$$x=\frac{-\left(-25\right)±\sqrt{593}}{2\times 8}$$

-25 ning teskarisi 25 ga teng.

$$x=\frac{25±\sqrt{593}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{25±\sqrt{593}}{16}$$

x=\frac{25±\sqrt{593}}{16} tenglamasini yeching, bunda ± musbat. 25 ni \sqrt{593} ga qo'shish.

$$x=\frac{\sqrt{593}+25}{16}$$

x=\frac{25±\sqrt{593}}{16} tenglamasini yeching, bunda ± manfiy. 25 dan \sqrt{593} ni ayirish.

$$x=\frac{25-\sqrt{593}}{16}$$

Tenglama yechildi.

$$x=\frac{\sqrt{593}+25}{16} x=\frac{25-\sqrt{593}}{16}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga, 2,4 ning eng kichik karralisiga ko‘paytiring.

$$4\times 2xx-2x+x+1=24x$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$8xx-2x+x+1=24x$$

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

$$8x^{2}-2x+x+1=24x$$

-x ni olish uchun -2x va x ni birlashtirish.

$$8x^{2}-x+1=24x$$

Ikkala tarafdan 24x ni ayirish.

$$8x^{2}-x+1-24x=0$$

-25x ni olish uchun -x va -24x ni birlashtirish.

$$8x^{2}-25x+1=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$8x^{2}-25x=-1$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8x^{2}-25x}{8}=-\frac{1}{8}$$

8 ga bo'lish 8 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{25}{8}x=-\frac{1}{8}$$

-\frac{25}{8} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{25}{16} olish uchun. Keyin, -\frac{25}{16} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{25}{8}x+\left(-\frac{25}{16}\right)^{2}=-\frac{1}{8}+\left(-\frac{25}{16}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{25}{16} kvadratini chiqarish.

$$x^{2}-\frac{25}{8}x+\frac{625}{256}=-\frac{1}{8}+\frac{625}{256}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{8} ni \frac{625}{256} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{25}{8}x+\frac{625}{256}=\frac{593}{256}$$

x^{2}-\frac{25}{8}x+\frac{625}{256} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{25}{16}\right)^{2}=\frac{593}{256}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{25}{16}\right)^{2}}=\sqrt{\frac{593}{256}}$$

Qisqartirish.

$$x-\frac{25}{16}=\frac{\sqrt{593}}{16} x-\frac{25}{16}=-\frac{\sqrt{593}}{16}$$

\frac{25}{16} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{593}+25}{16} x=\frac{25-\sqrt{593}}{16}$$