1/frac{1{x+10}+1/x}=720 eching

$$\frac{ 1 }{ \frac{ 1 }{ x+10 } + \frac{ 1 }{ x } } = 720$$

x uchun yechish

$$x=5\sqrt{20737}+715\approx 1435,017360902$$

$$x=715-5\sqrt{20737}\approx -5,017360902$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+10 va x ning eng kichik umumiy karralisi x\left(x+10\right). \frac{1}{x+10} ni \frac{x}{x} marotabaga ko'paytirish. \frac{1}{x} ni \frac{x+10}{x+10} marotabaga ko'paytirish.

$$\frac{1}{\frac{x}{x\left(x+10\right)}+\frac{x+10}{x\left(x+10\right)}}=720$$

\frac{x}{x\left(x+10\right)} va \frac{x+10}{x\left(x+10\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{\frac{x+x+10}{x\left(x+10\right)}}=720$$

x+x+10 kabi iboralarga o‘xshab birlashtiring.

$$\frac{1}{\frac{2x+10}{x\left(x+10\right)}}=720$$

x qiymati -10,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 1 ni \frac{2x+10}{x\left(x+10\right)} ga bo'lish 1 ga k'paytirish \frac{2x+10}{x\left(x+10\right)} ga qaytarish.

$$\frac{x\left(x+10\right)}{2x+10}=720$$

x ga x+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x^{2}+10x}{2x+10}=720$$

Ikkala tarafdan 720 ni ayirish.

$$\frac{x^{2}+10x}{2x+10}-720=0$$

Faktor: 2x+10.

$$\frac{x^{2}+10x}{2\left(x+5\right)}-720=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 720 ni \frac{2\left(x+5\right)}{2\left(x+5\right)} marotabaga ko'paytirish.

$$\frac{x^{2}+10x}{2\left(x+5\right)}-\frac{720\times 2\left(x+5\right)}{2\left(x+5\right)}=0$$

\frac{x^{2}+10x}{2\left(x+5\right)} va \frac{720\times 2\left(x+5\right)}{2\left(x+5\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x^{2}+10x-720\times 2\left(x+5\right)}{2\left(x+5\right)}=0$$

x^{2}+10x-720\times 2\left(x+5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+10x-1440x-7200}{2\left(x+5\right)}=0$$

x^{2}+10x-1440x-7200 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-1430x-7200}{2\left(x+5\right)}=0$$

x qiymati -5 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(x+5\right) ga ko'paytirish.

$$x^{2}-1430x-7200=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1430 ni b va -7200 ni c bilan almashtiring.

$$x=\frac{-\left(-1430\right)±\sqrt{\left(-1430\right)^{2}-4\left(-7200\right)}}{2}$$

-1430 kvadratini chiqarish.

$$x=\frac{-\left(-1430\right)±\sqrt{2044900-4\left(-7200\right)}}{2}$$

-4 ni -7200 marotabaga ko'paytirish.

$$x=\frac{-\left(-1430\right)±\sqrt{2044900+28800}}{2}$$

2044900 ni 28800 ga qo'shish.

$$x=\frac{-\left(-1430\right)±\sqrt{2073700}}{2}$$

2073700 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1430\right)±10\sqrt{20737}}{2}$$

-1430 ning teskarisi 1430 ga teng.

$$x=\frac{1430±10\sqrt{20737}}{2}$$

x=\frac{1430±10\sqrt{20737}}{2} tenglamasini yeching, bunda ± musbat. 1430 ni 10\sqrt{20737} ga qo'shish.

$$x=\frac{10\sqrt{20737}+1430}{2}$$

1430+10\sqrt{20737} ni 2 ga bo'lish.

$$x=5\sqrt{20737}+715$$

x=\frac{1430±10\sqrt{20737}}{2} tenglamasini yeching, bunda ± manfiy. 1430 dan 10\sqrt{20737} ni ayirish.

$$x=\frac{1430-10\sqrt{20737}}{2}$$

1430-10\sqrt{20737} ni 2 ga bo'lish.

$$x=715-5\sqrt{20737}$$

Tenglama yechildi.

$$x=5\sqrt{20737}+715 x=715-5\sqrt{20737}$$

Kvadratni yakunlash bo'yicha qadamlar

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+10 va x ning eng kichik umumiy karralisi x\left(x+10\right). \frac{1}{x+10} ni \frac{x}{x} marotabaga ko'paytirish. \frac{1}{x} ni \frac{x+10}{x+10} marotabaga ko'paytirish.

$$\frac{1}{\frac{x}{x\left(x+10\right)}+\frac{x+10}{x\left(x+10\right)}}=720$$

\frac{x}{x\left(x+10\right)} va \frac{x+10}{x\left(x+10\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{\frac{x+x+10}{x\left(x+10\right)}}=720$$

x+x+10 kabi iboralarga o‘xshab birlashtiring.

$$\frac{1}{\frac{2x+10}{x\left(x+10\right)}}=720$$

x qiymati -10,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. 1 ni \frac{2x+10}{x\left(x+10\right)} ga bo'lish 1 ga k'paytirish \frac{2x+10}{x\left(x+10\right)} ga qaytarish.

$$\frac{x\left(x+10\right)}{2x+10}=720$$

x ga x+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x^{2}+10x}{2x+10}=720$$

x qiymati -5 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2\left(x+5\right) ga ko'paytirish.

$$x^{2}+10x=1440\left(x+5\right)$$

1440 ga x+5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+10x=1440x+7200$$

Ikkala tarafdan 1440x ni ayirish.

$$x^{2}+10x-1440x=7200$$

-1430x ni olish uchun 10x va -1440x ni birlashtirish.

$$x^{2}-1430x=7200$$

-1430 ni bo‘lish, x shartining koeffitsienti, 2 ga -715 olish uchun. Keyin, -715 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-1430x+\left(-715\right)^{2}=7200+\left(-715\right)^{2}$$

-715 kvadratini chiqarish.

$$x^{2}-1430x+511225=7200+511225$$

7200 ni 511225 ga qo'shish.

$$x^{2}-1430x+511225=518425$$

x^{2}-1430x+511225 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-715\right)^{2}=518425$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-715\right)^{2}}=\sqrt{518425}$$

Qisqartirish.

$$x-715=5\sqrt{20737} x-715=-5\sqrt{20737}$$

715 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5\sqrt{20737}+715 x=715-5\sqrt{20737}$$