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What is the value of $ x^2 + 4y^2 + z^2 - 4xy +4 yz - 2xz $ ? |
$(x + 2y - z)^2 $ $(x - 2y + z)^2 $ $(2y - x + z)^2 $ $(2x - y + z)^2 $ |
$(2y - x + z)^2 $ |
$ x^2 + 4y^2 + z^2 - 4xy +4 yz - 2xz $ = x2 + (2y)2 + z2 - 2.(x).(2y) + 2.(z).(2y) - 2.(x).(z) = (-x)2 + (2y)2 + z2 + 2.(-x).(2y) + 2.(z).(2y) + 2.(-x).(z) Comparing with (a + b +c )2 = a2 + b2+ c2 + 2ab + 2bc + 2ca = (-x)2 + (2y)2 + z2 + 2.(-x).(2y) + 2.(z).(2y) + 2.(-x).(z) = (2y - x + z)2 |
