x uchun yechish
x=5\sqrt{20737}+725\approx 1445,017360902
x=725-5\sqrt{20737}\approx 4,982639098
Grafik
Viktorina
Quadratic Equation
5xshash muammolar:
\frac{ 1 }{ \frac{ 1 }{ x-10 } + \frac{ 1 }{ x } } = 720
Baham ko'rish
Klipbordga nusxa olish
\frac{1}{\frac{x}{x\left(x-10\right)}+\frac{x-10}{x\left(x-10\right)}}=720
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-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{2x-10}{x\left(x-10\right)}}=720
x+x-10 kabi iboralarga o‘xshab birlashtiring.
\frac{x\left(x-10\right)}{2x-10}=720
x qiymati 0,10 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^{2}-10x}{2x-10}=720
x ga x-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
\frac{x^{2}-10x}{2x-10}-720=0
Ikkala tarafdan 720 ni ayirish.
\frac{x^{2}-10x}{2\left(x-5\right)}-720=0
Faktor: 2x-10.
\frac{x^{2}-10x}{2\left(x-5\right)}-\frac{720\times 2\left(x-5\right)}{2\left(x-5\right)}=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-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-1440x+7200}{2\left(x-5\right)}=0
x^{2}-10x-720\times 2\left(x-5\right) ichidagi ko‘paytirishlarni bajaring.
\frac{x^{2}-1450x+7200}{2\left(x-5\right)}=0
x^{2}-10x-1440x+7200 kabi iboralarga o‘xshab birlashtiring.
x^{2}-1450x+7200=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=\frac{-\left(-1450\right)±\sqrt{\left(-1450\right)^{2}-4\times 7200}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1450 ni b va 7200 ni c bilan almashtiring.
x=\frac{-\left(-1450\right)±\sqrt{2102500-4\times 7200}}{2}
-1450 kvadratini chiqarish.
x=\frac{-\left(-1450\right)±\sqrt{2102500-28800}}{2}
-4 ni 7200 marotabaga ko'paytirish.
x=\frac{-\left(-1450\right)±\sqrt{2073700}}{2}
2102500 ni -28800 ga qo'shish.
x=\frac{-\left(-1450\right)±10\sqrt{20737}}{2}
2073700 ning kvadrat ildizini chiqarish.
x=\frac{1450±10\sqrt{20737}}{2}
-1450 ning teskarisi 1450 ga teng.
x=\frac{10\sqrt{20737}+1450}{2}
x=\frac{1450±10\sqrt{20737}}{2} tenglamasini yeching, bunda ± musbat. 1450 ni 10\sqrt{20737} ga qo'shish.
x=5\sqrt{20737}+725
1450+10\sqrt{20737} ni 2 ga bo'lish.
x=\frac{1450-10\sqrt{20737}}{2}
x=\frac{1450±10\sqrt{20737}}{2} tenglamasini yeching, bunda ± manfiy. 1450 dan 10\sqrt{20737} ni ayirish.
x=725-5\sqrt{20737}
1450-10\sqrt{20737} ni 2 ga bo'lish.
x=5\sqrt{20737}+725 x=725-5\sqrt{20737}
Tenglama yechildi.
\frac{1}{\frac{x}{x\left(x-10\right)}+\frac{x-10}{x\left(x-10\right)}}=720
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-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{2x-10}{x\left(x-10\right)}}=720
x+x-10 kabi iboralarga o‘xshab birlashtiring.
\frac{x\left(x-10\right)}{2x-10}=720
x qiymati 0,10 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^{2}-10x}{2x-10}=720
x ga x-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
x^{2}-10x=1440\left(x-5\right)
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=1440x-7200
1440 ga x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
x^{2}-10x-1440x=-7200
Ikkala tarafdan 1440x ni ayirish.
x^{2}-1450x=-7200
-1450x ni olish uchun -10x va -1440x ni birlashtirish.
x^{2}-1450x+\left(-725\right)^{2}=-7200+\left(-725\right)^{2}
-1450 ni bo‘lish, x shartining koeffitsienti, 2 ga -725 olish uchun. Keyin, -725 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}-1450x+525625=-7200+525625
-725 kvadratini chiqarish.
x^{2}-1450x+525625=518425
-7200 ni 525625 ga qo'shish.
\left(x-725\right)^{2}=518425
x^{2}-1450x+525625 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(x-725\right)^{2}}=\sqrt{518425}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-725=5\sqrt{20737} x-725=-5\sqrt{20737}
Qisqartirish.
x=5\sqrt{20737}+725 x=725-5\sqrt{20737}
725 ni tenglamaning ikkala tarafiga qo'shish.
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