2x+1/x-2+4/x=-8/x^2-2x eching

$$\frac { 2 x + 1 } { x - 2 } + \frac { 4 } { x } = \frac { - 8 } { x ^ { 2 } - 2 x }$$

x uchun yechish

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2,5$$

Faktorlash qadamlari

x qiymati 0,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-2\right) ga, x-2,x,x^{2}-2x ning eng kichik karralisiga ko‘paytiring.

$$x\left(2x+1\right)+\left(x-2\right)\times 4=-8$$

x ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+x+\left(x-2\right)\times 4=-8$$

x-2 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+x+4x-8=-8$$

5x ni olish uchun x va 4x ni birlashtirish.

$$2x^{2}+5x-8=-8$$

8 ni ikki tarafga qo’shing.

$$2x^{2}+5x-8+8=0$$

0 olish uchun -8 va 8'ni qo'shing.

$$2x^{2}+5x=0$$

x omili.

$$x\left(2x+5\right)=0$$

Tenglamani yechish uchun x=0 va 2x+5=0 ni yeching.

$$x=0 x=-\frac{5}{2}$$

x qiymati 0 teng bo‘lmaydi.

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

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-2\right) ga, x-2,x,x^{2}-2x ning eng kichik karralisiga ko‘paytiring.

$$x\left(2x+1\right)+\left(x-2\right)\times 4=-8$$

x ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+x+\left(x-2\right)\times 4=-8$$

x-2 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+x+4x-8=-8$$

5x ni olish uchun x va 4x ni birlashtirish.

$$2x^{2}+5x-8=-8$$

8 ni ikki tarafga qo’shing.

$$2x^{2}+5x-8+8=0$$

0 olish uchun -8 va 8'ni qo'shing.

$$2x^{2}+5x=0$$

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

$$x=\frac{-5±\sqrt{5^{2}}}{2\times 2}$$

5^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-5±5}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-5±5}{4}$$

x=\frac{-5±5}{4} tenglamasini yeching, bunda ± musbat. -5 ni 5 ga qo'shish.

$$x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x=0$$

x=\frac{-5±5}{4} tenglamasini yeching, bunda ± manfiy. -5 dan 5 ni ayirish.

$$x=-\frac{10}{4}$$

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

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

Tenglama yechildi.

$$x=0 x=-\frac{5}{2}$$

x qiymati 0 teng bo‘lmaydi.

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

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0,2 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-2\right) ga, x-2,x,x^{2}-2x ning eng kichik karralisiga ko‘paytiring.

$$x\left(2x+1\right)+\left(x-2\right)\times 4=-8$$

x ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+x+\left(x-2\right)\times 4=-8$$

x-2 ga 4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+x+4x-8=-8$$

5x ni olish uchun x va 4x ni birlashtirish.

$$2x^{2}+5x-8=-8$$

8 ni ikki tarafga qo’shing.

$$2x^{2}+5x=-8+8$$

0 olish uchun -8 va 8'ni qo'shing.

$$2x^{2}+5x=0$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+5x}{2}=\frac{0}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{5}{2}x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x^{2}+\frac{5}{2}x=0$$

\frac{5}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{5}{4} olish uchun. Keyin, \frac{5}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{5}{4} kvadratini chiqarish.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{25}{16}$$

x^{2}+\frac{5}{2}x+\frac{25}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{5}{4}\right)^{2}=\frac{25}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{\frac{25}{16}}$$

Qisqartirish.

$$x+\frac{5}{4}=\frac{5}{4} x+\frac{5}{4}=-\frac{5}{4}$$

Tenglamaning ikkala tarafidan \frac{5}{4} ni ayirish.

$$x=0 x=-\frac{5}{2}$$

x qiymati 0 teng bo‘lmaydi.

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