3x^2-8x+4x-2/x-2=5x+8 eching

$$\frac { 3 x ^ { 2 } - 8 x + 4 x - 2 } { x - 2 } = 5 x + 8$$

x uchun yechish

$$x = \frac{\sqrt{29} - 1}{2} \approx 2,192582404$$

$$x=\frac{-\sqrt{29}-1}{2}\approx -3,192582404$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-2 ga ko'paytirish.

$$3x^{2}-8x+4x-2=5x\left(x-2\right)+\left(x-2\right)\times 8$$

-4x ni olish uchun -8x va 4x ni birlashtirish.

$$3x^{2}-4x-2=5x\left(x-2\right)+\left(x-2\right)\times 8$$

5x ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-4x-2=5x^{2}-10x+\left(x-2\right)\times 8$$

x-2 ga 8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-4x-2=5x^{2}-10x+8x-16$$

-2x ni olish uchun -10x va 8x ni birlashtirish.

$$3x^{2}-4x-2=5x^{2}-2x-16$$

Ikkala tarafdan 5x^{2} ni ayirish.

$$3x^{2}-4x-2-5x^{2}=-2x-16$$

-2x^{2} ni olish uchun 3x^{2} va -5x^{2} ni birlashtirish.

$$-2x^{2}-4x-2=-2x-16$$

2x ni ikki tarafga qo’shing.

$$-2x^{2}-4x-2+2x=-16$$

-2x ni olish uchun -4x va 2x ni birlashtirish.

$$-2x^{2}-2x-2=-16$$

16 ni ikki tarafga qo’shing.

$$-2x^{2}-2x-2+16=0$$

14 olish uchun -2 va 16'ni qo'shing.

$$-2x^{2}-2x+14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, -2 ni b va 14 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-2\right)\times 14}}{2\left(-2\right)}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-2\right)\times 14}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+8\times 14}}{2\left(-2\right)}$$

8 ni 14 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+112}}{2\left(-2\right)}$$

4 ni 112 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{116}}{2\left(-2\right)}$$

116 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{29}}{2\left(-2\right)}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{29}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{29}}{-4}$$

x=\frac{2±2\sqrt{29}}{-4} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{29} ga qo'shish.

$$x=\frac{2\sqrt{29}+2}{-4}$$

2+2\sqrt{29} ni -4 ga bo'lish.

$$x=\frac{-\sqrt{29}-1}{2}$$

x=\frac{2±2\sqrt{29}}{-4} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{29} ni ayirish.

$$x=\frac{2-2\sqrt{29}}{-4}$$

2-2\sqrt{29} ni -4 ga bo'lish.

$$x=\frac{\sqrt{29}-1}{2}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{29}-1}{2} x=\frac{\sqrt{29}-1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x-2 ga ko'paytirish.

$$3x^{2}-8x+4x-2=5x\left(x-2\right)+\left(x-2\right)\times 8$$

-4x ni olish uchun -8x va 4x ni birlashtirish.

$$3x^{2}-4x-2=5x\left(x-2\right)+\left(x-2\right)\times 8$$

5x ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-4x-2=5x^{2}-10x+\left(x-2\right)\times 8$$

x-2 ga 8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-4x-2=5x^{2}-10x+8x-16$$

-2x ni olish uchun -10x va 8x ni birlashtirish.

$$3x^{2}-4x-2=5x^{2}-2x-16$$

Ikkala tarafdan 5x^{2} ni ayirish.

$$3x^{2}-4x-2-5x^{2}=-2x-16$$

-2x^{2} ni olish uchun 3x^{2} va -5x^{2} ni birlashtirish.

$$-2x^{2}-4x-2=-2x-16$$

2x ni ikki tarafga qo’shing.

$$-2x^{2}-4x-2+2x=-16$$

-2x ni olish uchun -4x va 2x ni birlashtirish.

$$-2x^{2}-2x-2=-16$$

2 ni ikki tarafga qo’shing.

$$-2x^{2}-2x=-16+2$$

-14 olish uchun -16 va 2'ni qo'shing.

$$-2x^{2}-2x=-14$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}-2x}{-2}=-\frac{14}{-2}$$

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

$$x^{2}+\left(-\frac{2}{-2}\right)x=-\frac{14}{-2}$$

-2 ni -2 ga bo'lish.

$$x^{2}+x=-\frac{14}{-2}$$

-14 ni -2 ga bo'lish.

$$x^{2}+x=7$$

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

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=7+\left(\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{2} kvadratini chiqarish.

$$x^{2}+x+\frac{1}{4}=7+\frac{1}{4}$$

7 ni \frac{1}{4} ga qo'shish.

$$x^{2}+x+\frac{1}{4}=\frac{29}{4}$$

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

$$\left(x+\frac{1}{2}\right)^{2}=\frac{29}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{29}{4}}$$

Qisqartirish.

$$x+\frac{1}{2}=\frac{\sqrt{29}}{2} x+\frac{1}{2}=-\frac{\sqrt{29}}{2}$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$x=\frac{\sqrt{29}-1}{2} x=\frac{-\sqrt{29}-1}{2}$$