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Byju's Answer
Standard VII
Mathematics
Finding the Value of an Expression
If x2+y2+z2...
Question
If
x
2
+
y
2
+
z
2
=
2
(
x
−
y
−
z
)
−
3
, find the value of
2
x
−
3
y
+
4
z
.
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Solution
Given,
x
2
+
y
2
+
z
2
=
2
(
x
−
y
−
z
)
−
3
⇒
(
x
2
−
2
x
)
+
(
y
2
+
2
y
)
+
(
z
2
+
2
z
)
+
3
=
0
⇒
(
x
2
−
2
x
+
1
)
+
(
y
2
+
2
y
+
1
)
+
(
z
2
+
2
z
+
1
)
=
0
⇒
(
x
−
1
)
2
+
(
y
+
1
)
2
+
(
z
+
1
)
2
=
0
⇒
(
x
−
1
)
=
0
and
(
y
+
1
)
=
0
and
(
z
+
1
)
=
0
⇒
x
=
1
and
y
=
−
1
and
z
=
−
1
∴
2
x
−
3
y
+
4
z
=
2
+
3
−
4
=
1
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1
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Q.
Let
S
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x
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