Question

Các bạn oi giúp mình tí, cmr:

(A+b+c)^2= a2+b2+c2+2ab+2bc+2ac

(A+b+c)^2+a^2+b^2+c^2=(a+b)^2+(b+c)^2+(c+a)^2

 

Answer 1

VT = (a+b+c)^2

= [(a+b) + c]^2

= (a+b)^2 + 2(a+b)c + c^2

= a^2 + 2ab + b^2 + 2ac + 2bc + c^2

= a^2 + b^2 + c^2 + 2ab + 2ac + 2bc = VP

Vậy ...

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VT= (a+b+c)^2 + a^2 + b^2 + c^2

= [(a+b) + c]^2 + a^2 + b^2 + c^2

= (a+b)^2 + 2(a+b)c + c^2 + a^2 + b^2 + c^2

= a^2 + 2ab + b^2 + 2ac + 2bc + c^2 + a^2 + b^2 + c^2

= (a^2 + 2ab + b^2) + (b^2 + 2bc + c^2) + (c^2 + 2ca + a^2)

= (a+b)^2 + (b+c)^2 + (c+a)^2 = VP

Vậy...

Answer 2

( a + b + c ) ² = a ( a + b + c ) + b ( a + b + c ) + c ( a + b + c ) 
= a² + ab + ac + ab + b² + bc + ac + bc + c²
= a² + b² + c² + 2ab + 2ac + 2bc