Question

Cho a+b+c=0 và a²+b²+c²=14.Tính Q=a⁴+b⁴+c4

Answer 1

Từ \(a+b+c=0\Leftrightarrow a^2+b^2+c^2=-2\left(ab+bc+ca\right)\)

\(\Leftrightarrow-7=ab+bc+ca\)\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)=49\)

\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2=49\left(\text{vi` a+b+c=0}\right)\)

Ma tu \(a^2+b^2+c^2=14\)

\(\Leftrightarrow a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=14^2\)

\(\Leftrightarrow a^4+b^4+c^4=14^2-2\cdot49=....\)