Toán cmr x^4+y^4+(x+y)^4=2(x^2+xy+y^2) giúp mk nhA!!!!!!! 08/07/2021 By Gabriella cmr x^4+y^4+(x+y)^4=2(x^2+xy+y^2) giúp mk nhA!!!!!!!
Ta có: $x^4 + y^4 + (x + y)^4$ $= x^4 + y^4 + [(x + y)^2]^2$ $= x^4 + y^4 + (x^2 + 2xy + y^2)^2$ $= x^4 + y^4 + x^4 + 4x^2y^2 + y^4 + 4x^3y + 4xy^3 + 2x^2y^2$ $=2(x^4 + y^4 + x^2y^2 + 2x^2y^2 + 2x^3y + 2xy^3)$ $= 2(x^2 + xy + y^2)^2$ Trả lời
Ta có:
$x^4 + y^4 + (x + y)^4$
$= x^4 + y^4 + [(x + y)^2]^2$
$= x^4 + y^4 + (x^2 + 2xy + y^2)^2$
$= x^4 + y^4 + x^4 + 4x^2y^2 + y^4 + 4x^3y + 4xy^3 + 2x^2y^2$
$=2(x^4 + y^4 + x^2y^2 + 2x^2y^2 + 2x^3y + 2xy^3)$
$= 2(x^2 + xy + y^2)^2$