76/a=left(15-hright)^3+k eching

$$\frac{ 76 }{ a } = { \left(15-h \right) }^{ 3 } +k$$

a uchun yechish

$$a=\frac{76}{\left(15-h\right)^{3}+k}$$

$$h\neq \sqrt[3]{k}+15$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

a qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini a ga ko'paytirish.

$$76=a\left(15-h\right)^{3}+ak$$

\left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} binom teoremasini \left(15-h\right)^{3} kengaytirilishi uchun ishlating.

$$76=a\left(3375-675h+45h^{2}-h^{3}\right)+ak$$

a ga 3375-675h+45h^{2}-h^{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$76=3375a-675ah+45ah^{2}-ah^{3}+ak$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$3375a-675ah+45ah^{2}-ah^{3}+ak=76$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3375-675h+45h^{2}-h^{3}+k\right)a=76$$

Tenglama standart shaklda.

$$\left(3375+k-675h+45h^{2}-h^{3}\right)a=76$$

Ikki tarafini 3375-675h+45h^{2}-h^{3}+k ga bo‘ling.

$$\frac{\left(3375+k-675h+45h^{2}-h^{3}\right)a}{3375+k-675h+45h^{2}-h^{3}}=\frac{76}{3375+k-675h+45h^{2}-h^{3}}$$

3375-675h+45h^{2}-h^{3}+k ga bo'lish 3375-675h+45h^{2}-h^{3}+k ga ko'paytirishni bekor qiladi.

$$a=\frac{76}{3375+k-675h+45h^{2}-h^{3}}$$

a qiymati 0 teng bo‘lmaydi.

$$a=\frac{76}{3375+k-675h+45h^{2}-h^{3}}\text{, }a\neq 0$$

h uchun yechish

$$h=-\sqrt[3]{-k+\frac{76}{a}}+15$$

$$a\neq 0$$