Question

Cho a+b+c =0 và a^2 + b^2 =14 . Tính M= a^4+b^4+c^4

Answer 1

thiếu c kìa

Answer 2

Ta có:\(a+b+c=0\)\(\Leftrightarrow a^2+b^2+c^2=-2\left(ab+bc+ca\right)\)\(\Leftrightarrow ab+bc+ca=-7\)\(\Leftrightarrow\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2+2abc\left(a+b+c\right)=49\)\(\Leftrightarrow\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2=49\)

Lại có:\(a^2+b^2+c^2=14\)

\(\Leftrightarrow a^4+b^4+c^4+2\left[\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2\right]=196\)

\(\Leftrightarrow a^4+b^4+c^4+98=196\)

\(\Leftrightarrow a^4+b^4+c^4=98\)