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

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

x uchun yechish (complex solution)

$$x=-5\sqrt{287}i+5\approx 5-84,70537173i$$

$$x=5+5\sqrt{287}i\approx 5+84,70537173i$$

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 0,10 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.

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

1 kvadratini chiqarish.

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

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

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

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

$$x=\frac{-1±\sqrt{1-288}}{2\left(-\frac{1}{10}\right)}$$

1 ni -288 ga qo'shish.

$$x=\frac{-1±\sqrt{-287}}{2\left(-\frac{1}{10}\right)}$$

-287 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±\sqrt{287}i}{2\left(-\frac{1}{10}\right)}$$

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

$$x=\frac{-1±\sqrt{287}i}{-\frac{1}{5}}$$

x=\frac{-1±\sqrt{287}i}{-\frac{1}{5}} tenglamasini yeching, bunda ± musbat. -1 ni i\sqrt{287} ga qo'shish.

$$x=\frac{-1+\sqrt{287}i}{-\frac{1}{5}}$$

-1+i\sqrt{287} ni -\frac{1}{5} ga bo'lish -1+i\sqrt{287} ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x=-5\sqrt{287}i+5$$

x=\frac{-1±\sqrt{287}i}{-\frac{1}{5}} tenglamasini yeching, bunda ± manfiy. -1 dan i\sqrt{287} ni ayirish.

$$x=\frac{-\sqrt{287}i-1}{-\frac{1}{5}}$$

-1-i\sqrt{287} ni -\frac{1}{5} ga bo'lish -1-i\sqrt{287} ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x=5+5\sqrt{287}i$$

Tenglama yechildi.

$$x=-5\sqrt{287}i+5 x=5+5\sqrt{287}i$$

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 0,10 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.

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

-5 kvadratini chiqarish.

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

-7200 ni 25 ga qo'shish.

$$x^{2}-10x+25=-7175$$

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.

$$\left(x-5\right)^{2}=-7175$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{-7175}$$

Qisqartirish.

$$x-5=5\sqrt{287}i x-5=-5\sqrt{287}i$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5+5\sqrt{287}i x=-5\sqrt{287}i+5$$