Question

if x = y cos(2π/3) = z cos(4π/3), then xy + yz + zx = ?
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Answer 1

Answer Let x = y cos 2pie by 3=z cos 4pie by 3 =k Then k/x = 1 ------(a) k/y = cos 2pie by 3 -------(b) k/z = cos 4pie by 3 -------(c)Now by adding (a) , (b) and (c) [k (yz + xz + xy)]/xyz = 1 + cos 2pie by 3 +cos 4pie by 3Taking L.C.M we get k (yz) + k (xz) + k (xy) = 1 + cos 2pie by 3 +cos 4pie by 3Now putting values of (cos 2pie by 3 ) and (cos 4pie by 3) we get[k (yz + xz + xy)]/xyz = 1-(1/2)-(1/2)Then[k (yz + xz + xy)]/xyz = 0k (yz + xz + xy) = 0yz + xz + xy = 0

Answer 2

please see the attachment