Question

Cho a-b=1 và a.b=12. Không tìm a và b hãy tính: a⁴+b⁴

Answer 1

\(a^4+b^4=a^4+4a^2b^2+b^4-4a^2b^2\)

\(=\left(a^2+b^2\right)-4a^2b^2\)

\(=\left[\left(a-b\right)^2-2ab\right]^2-4\cdot\left(ab\right)^2\)

\(=\left(1^2-2\cdot12\right)^2-4\cdot12^2\)

\(=\left(1-24\right)^2-4\cdot144\)

\(=\left(-23\right)^2-576=-47\)

Answer 2

\(a^2+b^2=\left(a-b\right)^2+2ab=1^2+2.12=25\)

\(a^4+b^4=\left(a^2+b^2\right)-2\left(ab\right)^2=25^2-2.12^2=337\)