If 3(u2+v2+w2)=(u+v+w2), find the value of -2u+v+w.
2 means square
Answers
Answer:
0
Step-by-step explanation:
Lets try to expand and solve the equation
3
(
u
2
+
v
2
+
w
2
)
=
(
u
+
v
+
w
)
2
.
3
(
u
2
+
v
2
+
w
2
)
=
(
u
+
v
+
w
)
2
⟹
3
(
u
2
+
v
2
+
w
2
)
=
u
2
+
v
2
+
w
2
+
2
u
v
+
2
v
w
+
2
w
u
⟹
3
(
u
2
+
v
2
+
w
2
)
−
(
u
2
+
v
2
+
w
2
)
=
2
u
v
+
2
v
w
+
2
w
u
⟹
(
u
2
+
v
2
+
w
2
)
(
3
−
1
)
=
2
u
v
+
2
v
w
+
2
w
u
⟹
2
(
u
2
+
v
2
+
w
2
)
=
2
(
u
v
+
v
w
+
w
u
)
⟹
u
2
+
v
2
+
w
2
=
u
v
+
v
w
+
w
u
⟹
u
2
+
v
2
+
w
2
−
u
v
−
v
w
−
w
u
=
0
⟹
u
2
−
u
v
+
v
2
−
v
w
+
w
2
−
w
u
=
0
⟹
u
(
u
−
v
)
+
v
(
v
−
w
)
+
w
(
w
−
u
)
=
0
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
From first possibility, we can infer u = v, v = w and w = u. This implies that u = v = w .
Second Possibility states that u = 0, v = 0, w = 0. Since this also satisfies the first possibility as well, therefore, u = v = w = 0.
Putting the values of u, v and w to 0 in expression u + v - 2w
u + v - 2w = 0