50/17*9800+34*9800h=26500(h^2-8875^2) eching

$$\frac { 50 } { 17 } \times 9800 + 34 \times 9800 h = 26500 ( h ^ { 2 } - 8875 ^ { 2 } )$$

h uchun yechish

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx 8881,289080421$$

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx -8868,715495515$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{490000}{17} hosil qilish uchun \frac{50}{17} va 9800 ni ko'paytirish.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

333200 hosil qilish uchun 34 va 9800 ni ko'paytirish.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

2 daraja ko‘rsatkichini 8875 ga hisoblang va 78765625 ni qiymatni oling.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

26500 ga h^{2}-78765625 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Ikkala tarafdan 26500h^{2} ni ayirish.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

2087289062500 ni ikki tarafga qo’shing.

$$\frac{490000}{17}+333200h-26500h^{2}[phone]=0$$

\frac{35483914552500}{17} olish uchun \frac{490000}{17} va 2087289062500'ni qo'shing.

$$\frac{35483914552500}{17}+333200h-26500h^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-26500h^{2}+333200h+\frac{35483914552500}{17}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -26500 ni a, 333200 ni b va \frac{35483914552500}{17} ni c bilan almashtiring.

$$h=\frac{-333200±\sqrt{333200^{2}-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

333200 kvadratini chiqarish.

$$h=\frac{-333200±\sqrt{111022240000-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

-4 ni -26500 marotabaga ko'paytirish.

$$h=\frac{-333200±\sqrt{111022240000+106000\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

106000 ni \frac{35483914552500}{17} marotabaga ko'paytirish.

$$h=\frac{-333200±\sqrt{111022240000+\frac{3761294942565000000}{17}}}{2\left(-26500\right)}$$

111022240000 ni \frac{3761294942565000000}{17} ga qo'shish.

$$h=\frac{-333200±\sqrt{\frac{3761296829943080000}{17}}}{2\left(-26500\right)}$$

\frac{3761296829943080000}{17} ning kvadrat ildizini chiqarish.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{2\left(-26500\right)}$$

2 ni -26500 marotabaga ko'paytirish.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000}$$

h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} tenglamasini yeching, bunda ± musbat. -333200 ni \frac{200\sqrt{1598551152725809}}{17} ga qo'shish.

$$h=\frac{\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

-333200+\frac{200\sqrt{1598551152725809}}{17} ni -53000 ga bo'lish.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} tenglamasini yeching, bunda ± manfiy. -333200 dan \frac{200\sqrt{1598551152725809}}{17} ni ayirish.

$$h=\frac{-\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

-333200-\frac{200\sqrt{1598551152725809}}{17} ni -53000 ga bo'lish.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Tenglama yechildi.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Kvadratni yakunlash bo'yicha qadamlar

\frac{490000}{17} hosil qilish uchun \frac{50}{17} va 9800 ni ko'paytirish.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

333200 hosil qilish uchun 34 va 9800 ni ko'paytirish.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

2 daraja ko‘rsatkichini 8875 ga hisoblang va 78765625 ni qiymatni oling.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

26500 ga h^{2}-78765625 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Ikkala tarafdan 26500h^{2} ni ayirish.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

Ikkala tarafdan \frac{490000}{17} ni ayirish.

$$333200h-26500h^{2}=-2087289062500-\frac{490000}{17}$$

-\frac{35483914552500}{17} olish uchun -2087289062500 dan \frac{490000}{17} ni ayirish.

$$333200h-26500h^{2}=-\frac{35483914552500}{17}$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-26500h^{2}+333200h=-\frac{35483914552500}{17}$$

Ikki tarafini -26500 ga bo‘ling.

$$\frac{-26500h^{2}+333200h}{-26500}=-\frac{\frac{35483914552500}{17}}{-26500}$$

-26500 ga bo'lish -26500 ga ko'paytirishni bekor qiladi.

$$h^{2}+\frac{333200}{-26500}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

\frac{333200}{-26500} ulushini 100 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$h^{2}-\frac{3332}{265}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

-\frac{35483914552500}{17} ni -26500 ga bo'lish.

$$h^{2}-\frac{3332}{265}h=\frac{70967829105}{901}$$

-\frac{3332}{265} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1666}{265} olish uchun. Keyin, -\frac{1666}{265} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$h^{2}-\frac{3332}{265}h+\left(-\frac{1666}{265}\right)^{2}=\frac{70967829105}{901}+\left(-\frac{1666}{265}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1666}{265} kvadratini chiqarish.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{70967829105}{901}+\frac{2775556}{70225}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{70967829105}{901} ni \frac{2775556}{70225} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{94032420748577}{1193825}$$

h^{2}-\frac{3332}{265}h+\frac{2775556}{70225} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(h-\frac{1666}{265}\right)^{2}=\frac{94032420748577}{1193825}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(h-\frac{1666}{265}\right)^{2}}=\sqrt{\frac{94032420748577}{1193825}}$$

Qisqartirish.

$$h-\frac{1666}{265}=\frac{\sqrt{1598551152725809}}{4505} h-\frac{1666}{265}=-\frac{\sqrt{1598551152725809}}{4505}$$

\frac{1666}{265} ni tenglamaning ikkala tarafiga qo'shish.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$