CMR: a2 b2 c2 d2 = a(bcd)

Question

CMR: a^2 + b^2 +c^2 +d^2 >= a(b+c+d)

baoquyen · Answer

Biện ph&aacute;p: Chứng minh tương đương    Ta c&oacute; : a&sup2;+b&sup2;+c&sup2;+d&sup2;&ge;a(b+c+d)   &hArr;4a&sup2;+4b&sup2;+4c&sup2;+4d&sup2;&ge;4ab+4ac+4ad   &hArr;(a&sup2;-4ab+4b&sup2;)+(a&sup2;-4ac+4c&sup2;)+(a&sup2;-4ad+4d&sup2;)+a&sup2;&ge;0   &hArr;(a-2b)&sup2;+(a-2c)&sup2;+(a-2d)&sup2;+a&sup2;&ge;0 (lu&ocirc;n đ&uacute;ng)   Vậy a&sup2;+b&sup2;+c&sup2;+d&sup2;&ge;a(b+c+d)

CMR: a^2 + b^2 +c^2 +d^2 >= a(b+c+d)

1 bình luận về “CMR: a^2 + b^2 +c^2 +d^2 >= a(b+c+d)”

Viết một bình luận Hủy