(-5+8a^3)^2=I eching

$$( - 5 + 8 a ^ { 3 } ) ^ { 2 } = I$$

I uchun yechish

$$I=\left(8a^{3}-5\right)^{2}$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(-5+8a^{3}\right)^{2} kengaytirilishi uchun ishlating.

$$25-80a^{3}+64\left(a^{3}\right)^{2}=I$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

$$25-80a^{3}+64a^{6}=I$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$I=25-80a^{3}+64a^{6}$$

a uchun yechish

$$a=\frac{\sqrt[3]{-\sqrt{I}+5}}{2}$$

$$a=\frac{\sqrt[3]{\sqrt{I}+5}}{2}\text{, }I\geq 0$$