1) Viết thành tổng 3 bình phương: a) \(\left(a+b+c\right)^2+a^2+b^2+c^2\) b) \(2\left(a-b\right)\left(c-b\right)+2\left(b-a\right)\left(c-a\right)+2\left(b-c\right)\left(a-c\right)\)2) Cho \(a+b+c=0\)\(CMR\) a) \(a^4+b^4+c^2=2\left(a^2b^2+b^2c^2+c^2a^2\right)\) ...
Đọc tiếp
1) Viết thành tổng 3 bình phương:
a) \(\left(a+b+c\right)^2+a^2+b^2+c^2\)
b) \(2\left(a-b\right)\left(c-b\right)+2\left(b-a\right)\left(c-a\right)+2\left(b-c\right)\left(a-c\right)\)
2) Cho \(a+b+c=0\)\(CMR\)
a) \(a^4+b^4+c^2=2\left(a^2b^2+b^2c^2+c^2a^2\right)\)
b) \(2\left(ab+bc+ca\right)^2=2\left(a^2b^2+b^2c^2+c^2a^2\right)\)
1a) a2 + b2 + c2 + 2ab + 2bc + 2ca + a2 + b2 + c2
= ( a2 + 2ab +b2 ) + ( a2 + 2ac + c2 ) + ( b2 + 2bc + c2 )
= ( a + b )2 + ( a + c )2 + ( b + c )2
1b) 2.( ac - ab - bc + b2 ) + 2.( bc - ba - ac + a2 ) + 2.( ba - bc - ca + c2 )
= 2ac - 2ab - 2bc + 2b2 + 2bc - 2ab - 2ac +2a2 + 2ab - 2bc - 2ac + 2c2
= 2a2 + 2b2 + 2c2 - 2ab - 2ac - 2bc
= ( a2 - 2ab + b2 ) + (a2 - 2ac + c2 ) + (b2 - 2bc + c2 )
= (a-b)2 + (a-c)2 + (b-c)2