20000=10000*1.015^8+x*1.015^3 eching

$$20000 = 10000 \cdot 1.015 ^ { 8 } + x \cdot 1.015 ^ { 3 }$$

x uchun yechish

$$x = \frac{2236178978316014239}{267693664000000} = 8353\frac{133802924014336}{267693664000000} \approx 8353,499835977$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

8 daraja ko‘rsatkichini 1,015 ga hisoblang va 1,126492586595306937890625 ni qiymatni oling.

$$20000=10000\times 1,126492586595306937890625+x\times 1,015^{3}$$

11264,92586595306937890625 hosil qilish uchun 10000 va 1,126492586595306937890625 ni ko'paytirish.

$$20000=11264,92586595306937890625+x\times 1,015^{3}$$

3 daraja ko‘rsatkichini 1,015 ga hisoblang va 1,045678375 ni qiymatni oling.

$$20000=11264,92586595306937890625+x\times 1,045678375$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$11264,92586595306937890625+x\times 1,045678375=20000$$

Ikkala tarafdan 11264,92586595306937890625 ni ayirish.

$$x\times 1,045678375=20000-11264,92586595306937890625$$

8735,07413404693062109375 olish uchun 20000 dan 11264,92586595306937890625 ni ayirish.

$$x\times 1,045678375=8735,07413404693062109375$$

Ikki tarafini 1,045678375 ga bo‘ling.

$$x=\frac{8735,07413404693062109375}{1,045678375}$$

\frac{8735,07413404693062109375}{1,045678375} kasrini uning surat va maxrajini 100000000000000000000 ga ko‘paytirish bilan kengaytiring.

$$x=\frac{873507413404693062109375}{104567837500000000000}$$

\frac{873507413404693062109375}{104567837500000000000} ulushini 390625 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{2236178978316014239}{267693664000000}$$