Question

若三角形的三边A B C ,且满足A的4次方+B的4次方+C的4次方=A的2次方乘B的2次方+B的2次方乘C的2次方+C

Answer 1

1.

A^4+B^4+C^4=A^2B^2+B^2C^2+C^2A^2

2A^4+2B^4+2C^4=2A^2B^2+2B^2C^2+2C^2A^2

A^4-2A^2B^2+B^4+A^4-2C^2A^2+C^4+B^4-2B^2C^2+C^4=0

(A^2-B^2)^2+(A^2-C^2)^2+(B^2-C^2)^2=0

A^2-B^2=0,A^2-C^2=0,B^2-C^2=0

A^2=B^2=C^2

A=B=C

该三角形为等边三角形.

2.

M^2+M-1=0

M^2+M=1

M^3+2M^2+2005

=M(M^2+M)+M^2+2005

=M+M^2+2005

=1+2005

=2006