If 3(u2+v2+w2)=(u+v+w)2, find the value of u+v2w.


Answer:

0

Step by Step Explanation:
  1. Lets try to expand and solve the equation 3(u2+v2+w2)=(u+v+w)2.
  2. 3(u2+v2+w2)=(u+v+w)23(u2+v2+w2)=u2+v2+w2+2uv+2vw+2wu3(u2+v2+w2)(u2+v2+w2)=2uv+2vw+2wu(u2+v2+w2)(31)=2uv+2vw+2wu2(u2+v2+w2)=2(uv+vw+wu)u2+v2+w2=uv+vw+wuu2+v2+w2uvvwwu=0u2uv+v2vw+w2wu=0u(uv)+v(vw)+w(wu)=0
  3. As can be seen from above equation, for right hand side to be zero, there are only two possibilities. Either
    (u - v) = 0, (v - w) = 0 and (w - u) = 0 ..... I
    OR
    u = 0, v = 0 and w = 0 ..... II
  4. From first possibility, we can infer u = v, v = w and w = u. This implies that u = v = w .
  5. Second Possibility states that u = 0, v = 0, w = 0. Since this also satisfies the first possibility as well, therefore, u = v = w = 0.
  6. Putting the values of u, v and w to 0 in expression u + v - 2w
    u + v - 2w = 0

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