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

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

x uchun yechish

$$x=-90$$

$$x=80$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

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

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

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

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

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

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

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

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

\frac{1}{10}x^{2}+x natijani olish uchun x^{2}+10x ning har bir ifodasini 10 ga bo‘ling.

$$\frac{1}{10}x^{2}+x=720$$

Ikkala tarafdan 720 ni ayirish.

$$\frac{1}{10}x^{2}+x-720=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{10} ni a, 1 ni b va -720 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\times \frac{1}{10}\left(-720\right)}}{2\times \frac{1}{10}}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\times \frac{1}{10}\left(-720\right)}}{2\times \frac{1}{10}}$$

-4 ni \frac{1}{10} marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1-\frac{2}{5}\left(-720\right)}}{2\times \frac{1}{10}}$$

-\frac{2}{5} ni -720 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+288}}{2\times \frac{1}{10}}$$

1 ni 288 ga qo'shish.

$$x=\frac{-1±\sqrt{289}}{2\times \frac{1}{10}}$$

289 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±17}{2\times \frac{1}{10}}$$

2 ni \frac{1}{10} marotabaga ko'paytirish.

$$x=\frac{-1±17}{\frac{1}{5}}$$

x=\frac{-1±17}{\frac{1}{5}} tenglamasini yeching, bunda ± musbat. -1 ni 17 ga qo'shish.

$$x=\frac{16}{\frac{1}{5}}$$

16 ni \frac{1}{5} ga bo'lish 16 ga k'paytirish \frac{1}{5} ga qaytarish.

$$x=80$$

x=\frac{-1±17}{\frac{1}{5}} tenglamasini yeching, bunda ± manfiy. -1 dan 17 ni ayirish.

$$x=-\frac{18}{\frac{1}{5}}$$

-18 ni \frac{1}{5} ga bo'lish -18 ga k'paytirish \frac{1}{5} ga qaytarish.

$$x=-90$$

Tenglama yechildi.

$$x=80 x=-90$$

Kvadratni yakunlash bo'yicha qadamlar

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

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

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

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

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

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

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

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

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

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

\frac{1}{10}x^{2}+x natijani olish uchun x^{2}+10x ning har bir ifodasini 10 ga bo‘ling.

$$\frac{1}{10}x^{2}+x=720$$

Ikkala tarafini 10 ga ko‘paytiring.

$$\frac{\frac{1}{10}x^{2}+x}{\frac{1}{10}}=\frac{720}{\frac{1}{10}}$$

\frac{1}{10} ga bo'lish \frac{1}{10} ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1}{\frac{1}{10}}x=\frac{720}{\frac{1}{10}}$$

1 ni \frac{1}{10} ga bo'lish 1 ga k'paytirish \frac{1}{10} ga qaytarish.

$$x^{2}+10x=\frac{720}{\frac{1}{10}}$$

720 ni \frac{1}{10} ga bo'lish 720 ga k'paytirish \frac{1}{10} ga qaytarish.

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

10 ni bo‘lish, x shartining koeffitsienti, 2 ga 5 olish uchun. Keyin, 5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+10x+5^{2}=7200+5^{2}$$

5 kvadratini chiqarish.

$$x^{2}+10x+25=7200+25$$

7200 ni 25 ga qo'shish.

$$x^{2}+10x+25=7225$$

x^{2}+10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+5\right)^{2}=7225$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{7225}$$

Qisqartirish.

$$x+5=85 x+5=-85$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$x=80 x=-90$$