x-3=11/x-2-5 eching

$$x - 3 = \frac { 11 } { x - 2 } - 5$$

x uchun yechish

$$x=\sqrt{15}\approx 3,872983346$$

$$x=-\sqrt{15}\approx -3,872983346$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$\left(x-2\right)x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-2x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

x-2 ga -3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-2x-3x+6=11+\left(x-2\right)\left(-5\right)$$

-5x ni olish uchun -2x va -3x ni birlashtirish.

$$x^{2}-5x+6=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-5x+6=11-5x+10$$

21 olish uchun 11 va 10'ni qo'shing.

$$x^{2}-5x+6=21-5x$$

5x ni ikki tarafga qo’shing.

$$x^{2}-5x+6+5x=21$$

0 ni olish uchun -5x va 5x ni birlashtirish.

$$x^{2}+6=21$$

Ikkala tarafdan 6 ni ayirish.

$$x^{2}=21-6$$

15 olish uchun 21 dan 6 ni ayirish.

$$x^{2}=15$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{15} x=-\sqrt{15}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$\left(x-2\right)x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-2x+\left(x-2\right)\left(-3\right)=11+\left(x-2\right)\left(-5\right)$$

x-2 ga -3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-2x-3x+6=11+\left(x-2\right)\left(-5\right)$$

-5x ni olish uchun -2x va -3x ni birlashtirish.

$$x^{2}-5x+6=11+\left(x-2\right)\left(-5\right)$$

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

$$x^{2}-5x+6=11-5x+10$$

21 olish uchun 11 va 10'ni qo'shing.

$$x^{2}-5x+6=21-5x$$

Ikkala tarafdan 21 ni ayirish.

$$x^{2}-5x+6-21=-5x$$

-15 olish uchun 6 dan 21 ni ayirish.

$$x^{2}-5x-15=-5x$$

5x ni ikki tarafga qo’shing.

$$x^{2}-5x-15+5x=0$$

0 ni olish uchun -5x va 5x ni birlashtirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -15 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-15\right)}}{2}$$

-4 ni -15 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{60}}{2}$$

60 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{15}}{2}$$

x=\frac{0±2\sqrt{15}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{15}$$

x=\frac{0±2\sqrt{15}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{15}$$

Tenglama yechildi.

$$x=\sqrt{15} x=-\sqrt{15}$$