36/x-6-36/x=1/5 eching

$$\frac { 36 } { x - 6 } - \frac { 36 } { x } = \frac { 1 } { 5 }$$

x uchun yechish

$$x=-30$$

$$x=36$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0,6 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x\left(x-6\right) ga, x-6,x,5 ning eng kichik karralisiga ko‘paytiring.

$$5x\times 36-\left(5x-30\right)\times 36=x\left(x-6\right)$$

180 hosil qilish uchun 5 va 36 ni ko'paytirish.

$$180x-\left(5x-30\right)\times 36=x\left(x-6\right)$$

5x-30 ga 36 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180x-\left(180x-1080\right)=x\left(x-6\right)$$

180x-1080 teskarisini topish uchun har birining teskarisini toping.

$$180x-180x+1080=x\left(x-6\right)$$

0 ni olish uchun 180x va -180x ni birlashtirish.

$$1080=x\left(x-6\right)$$

x ga x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1080=x^{2}-6x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-6x=1080$$

Ikkala tarafdan 1080 ni ayirish.

$$x^{2}-6x-1080=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va -1080 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1080\right)}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1080\right)}}{2}$$

-4 ni -1080 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+4320}}{2}$$

36 ni 4320 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{4356}}{2}$$

4356 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±66}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±66}{2}$$

x=\frac{6±66}{2} tenglamasini yeching, bunda ± musbat. 6 ni 66 ga qo'shish.

$$x=\frac{72}{2}$$

72 ni 2 ga bo'lish.

$$x=36$$

x=\frac{6±66}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 66 ni ayirish.

$$x=-\frac{60}{2}$$

-60 ni 2 ga bo'lish.

$$x=-30$$

Tenglama yechildi.

$$x=36 x=-30$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0,6 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x\left(x-6\right) ga, x-6,x,5 ning eng kichik karralisiga ko‘paytiring.

$$5x\times 36-\left(5x-30\right)\times 36=x\left(x-6\right)$$

180 hosil qilish uchun 5 va 36 ni ko'paytirish.

$$180x-\left(5x-30\right)\times 36=x\left(x-6\right)$$

5x-30 ga 36 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$180x-\left(180x-1080\right)=x\left(x-6\right)$$

180x-1080 teskarisini topish uchun har birining teskarisini toping.

$$180x-180x+1080=x\left(x-6\right)$$

0 ni olish uchun 180x va -180x ni birlashtirish.

$$1080=x\left(x-6\right)$$

x ga x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1080=x^{2}-6x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-6x=1080$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=1080+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=1080+9$$

1080 ni 9 ga qo'shish.

$$x^{2}-6x+9=1089$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=1089$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{1089}$$

Qisqartirish.

$$x-3=33 x-3=-33$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=36 x=-30$$