2/1=(12+h)^2/12^2 eching

$$\frac { 2 } { 1 } = \frac { ( 12 + h ) ^ { 2 } } { 12 ^ { 2 } }$$

h uchun yechish

$$h=12\sqrt{2}-12\approx 4,970562748$$

$$h=-12\sqrt{2}-12\approx -28,970562748$$

Kvadrat tenglamalaridan foydalanish qoidalari

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$2=\frac{\left(12+h\right)^{2}}{12^{2}}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(12+h\right)^{2} kengaytirilishi uchun ishlating.

$$2=\frac{144+24h+h^{2}}{12^{2}}$$

2 daraja ko‘rsatkichini 12 ga hisoblang va 144 ni qiymatni oling.

$$2=\frac{144+24h+h^{2}}{144}$$

1+\frac{1}{6}h+\frac{1}{144}h^{2} natijani olish uchun 144+24h+h^{2} ning har bir ifodasini 144 ga bo‘ling.

$$2=1+\frac{1}{6}h+\frac{1}{144}h^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1+\frac{1}{6}h+\frac{1}{144}h^{2}=2$$

Ikkala tarafdan 2 ni ayirish.

$$1+\frac{1}{6}h+\frac{1}{144}h^{2}-2=0$$

-1 olish uchun 1 dan 2 ni ayirish.

$$-1+\frac{1}{6}h+\frac{1}{144}h^{2}=0$$

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.

$$\frac{1}{144}h^{2}+\frac{1}{6}h-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{144} ni a, \frac{1}{6} ni b va -1 ni c bilan almashtiring.

$$h=\frac{-\frac{1}{6}±\sqrt{\left(\frac{1}{6}\right)^{2}-4\times \frac{1}{144}\left(-1\right)}}{2\times \frac{1}{144}}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{6} kvadratini chiqarish.

$$h=\frac{-\frac{1}{6}±\sqrt{\frac{1}{36}-4\times \frac{1}{144}\left(-1\right)}}{2\times \frac{1}{144}}$$

-4 ni \frac{1}{144} marotabaga ko'paytirish.

$$h=\frac{-\frac{1}{6}±\sqrt{\frac{1}{36}-\frac{1}{36}\left(-1\right)}}{2\times \frac{1}{144}}$$

-\frac{1}{36} ni -1 marotabaga ko'paytirish.

$$h=\frac{-\frac{1}{6}±\sqrt{\frac{1+1}{36}}}{2\times \frac{1}{144}}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{36} ni \frac{1}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$h=\frac{-\frac{1}{6}±\sqrt{\frac{1}{18}}}{2\times \frac{1}{144}}$$

\frac{1}{18} ning kvadrat ildizini chiqarish.

$$h=\frac{-\frac{1}{6}±\frac{\sqrt{2}}{6}}{2\times \frac{1}{144}}$$

2 ni \frac{1}{144} marotabaga ko'paytirish.

$$h=\frac{-\frac{1}{6}±\frac{\sqrt{2}}{6}}{\frac{1}{72}}$$

h=\frac{-\frac{1}{6}±\frac{\sqrt{2}}{6}}{\frac{1}{72}} tenglamasini yeching, bunda ± musbat. -\frac{1}{6} ni \frac{\sqrt{2}}{6} ga qo'shish.

$$h=\frac{\sqrt{2}-1}{\frac{1}{72}\times 6}$$

\frac{-1+\sqrt{2}}{6} ni \frac{1}{72} ga bo'lish \frac{-1+\sqrt{2}}{6} ga k'paytirish \frac{1}{72} ga qaytarish.

$$h=12\sqrt{2}-12$$

h=\frac{-\frac{1}{6}±\frac{\sqrt{2}}{6}}{\frac{1}{72}} tenglamasini yeching, bunda ± manfiy. -\frac{1}{6} dan \frac{\sqrt{2}}{6} ni ayirish.

$$h=\frac{-\sqrt{2}-1}{\frac{1}{72}\times 6}$$

\frac{-1-\sqrt{2}}{6} ni \frac{1}{72} ga bo'lish \frac{-1-\sqrt{2}}{6} ga k'paytirish \frac{1}{72} ga qaytarish.

$$h=-12\sqrt{2}-12$$

Tenglama yechildi.

$$h=12\sqrt{2}-12 h=-12\sqrt{2}-12$$

Kvadratni yakunlash bo'yicha qadamlar

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$2=\frac{\left(12+h\right)^{2}}{12^{2}}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(12+h\right)^{2} kengaytirilishi uchun ishlating.

$$2=\frac{144+24h+h^{2}}{12^{2}}$$

2 daraja ko‘rsatkichini 12 ga hisoblang va 144 ni qiymatni oling.

$$2=\frac{144+24h+h^{2}}{144}$$

1+\frac{1}{6}h+\frac{1}{144}h^{2} natijani olish uchun 144+24h+h^{2} ning har bir ifodasini 144 ga bo‘ling.

$$2=1+\frac{1}{6}h+\frac{1}{144}h^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$1+\frac{1}{6}h+\frac{1}{144}h^{2}=2$$

Ikkala tarafdan 1 ni ayirish.

$$\frac{1}{6}h+\frac{1}{144}h^{2}=2-1$$

1 olish uchun 2 dan 1 ni ayirish.

$$\frac{1}{6}h+\frac{1}{144}h^{2}=1$$

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

$$\frac{1}{144}h^{2}+\frac{1}{6}h=1$$

Ikkala tarafini 144 ga ko‘paytiring.

$$\frac{\frac{1}{144}h^{2}+\frac{1}{6}h}{\frac{1}{144}}=\frac{1}{\frac{1}{144}}$$

\frac{1}{144} ga bo'lish \frac{1}{144} ga ko'paytirishni bekor qiladi.

$$h^{2}+\frac{\frac{1}{6}}{\frac{1}{144}}h=\frac{1}{\frac{1}{144}}$$

\frac{1}{6} ni \frac{1}{144} ga bo'lish \frac{1}{6} ga k'paytirish \frac{1}{144} ga qaytarish.

$$h^{2}+24h=\frac{1}{\frac{1}{144}}$$

1 ni \frac{1}{144} ga bo'lish 1 ga k'paytirish \frac{1}{144} ga qaytarish.

$$h^{2}+24h=144$$

24 ni bo‘lish, x shartining koeffitsienti, 2 ga 12 olish uchun. Keyin, 12 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$h^{2}+24h+12^{2}=144+12^{2}$$

12 kvadratini chiqarish.

$$h^{2}+24h+144=144+144$$

144 ni 144 ga qo'shish.

$$h^{2}+24h+144=288$$

h^{2}+24h+144 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(h+12\right)^{2}=288$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(h+12\right)^{2}}=\sqrt{288}$$

Qisqartirish.

$$h+12=12\sqrt{2} h+12=-12\sqrt{2}$$

Tenglamaning ikkala tarafidan 12 ni ayirish.

$$h=12\sqrt{2}-12 h=-12\sqrt{2}-12$$