9/x-3-27/x(x-3)=-3 eching

$$\frac { 9 } { x - 3 } - \frac { 27 } { x ( x - 3 ) } = - 3$$

x uchun yechish

$$x=-3$$

Kvadratlar farqidan foydalangan qadamlar

x qiymati 0,3 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-3\right) ga, x-3,x\left(x-3\right) ning eng kichik karralisiga ko‘paytiring.

$$x\times 9-27=-3x\left(x-3\right)$$

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

$$x\times 9-27=-3x^{2}+9x$$

3x^{2} ni ikki tarafga qo’shing.

$$x\times 9-27+3x^{2}=9x$$

Ikkala tarafdan 9x ni ayirish.

$$x\times 9-27+3x^{2}-9x=0$$

0 ni olish uchun x\times 9 va -9x ni birlashtirish.

$$-27+3x^{2}=0$$

Ikki tarafini 3 ga bo‘ling.

$$-9+x^{2}=0$$

Hisoblang: -9+x^{2}. -9+x^{2} ni x^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

Tenglamani yechish uchun x-3=0 va x+3=0 ni yeching.

$$x=3 x=-3$$

x qiymati 3 teng bo‘lmaydi.

$$x=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati 0,3 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-3\right) ga, x-3,x\left(x-3\right) ning eng kichik karralisiga ko‘paytiring.

$$x\times 9-27=-3x\left(x-3\right)$$

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

$$x\times 9-27=-3x^{2}+9x$$

3x^{2} ni ikki tarafga qo’shing.

$$x\times 9-27+3x^{2}=9x$$

Ikkala tarafdan 9x ni ayirish.

$$x\times 9-27+3x^{2}-9x=0$$

0 ni olish uchun x\times 9 va -9x ni birlashtirish.

$$-27+3x^{2}=0$$

27 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$3x^{2}=27$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{27}{3}$$

9 ni olish uchun 27 ni 3 ga bo‘ling.

$$x^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3 x=-3$$

x qiymati 3 teng bo‘lmaydi.

$$x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0,3 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x\left(x-3\right) ga, x-3,x\left(x-3\right) ning eng kichik karralisiga ko‘paytiring.

$$x\times 9-27=-3x\left(x-3\right)$$

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

$$x\times 9-27=-3x^{2}+9x$$

3x^{2} ni ikki tarafga qo’shing.

$$x\times 9-27+3x^{2}=9x$$

Ikkala tarafdan 9x ni ayirish.

$$x\times 9-27+3x^{2}-9x=0$$

0 ni olish uchun x\times 9 va -9x ni birlashtirish.

$$-27+3x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$3x^{2}-27=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -27 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-27\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-27\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-27\right)}}{2\times 3}$$

-12 ni -27 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{324}}{2\times 3}$$

324 ning kvadrat ildizini chiqarish.

$$x=\frac{0±18}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±18}{6}$$

x=\frac{0±18}{6} tenglamasini yeching, bunda ± musbat. 18 ni 6 ga bo'lish.

$$x=3$$

x=\frac{0±18}{6} tenglamasini yeching, bunda ± manfiy. -18 ni 6 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=3 x=-3$$

x qiymati 3 teng bo‘lmaydi.

$$x=-3$$