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Algebra and Applications Test 1
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© examsnet.com
Question : 24
Total: 40
If x = a - b, y = b - c, z = c - a, then the numerical value of the algebraic expression
x
3
+
y
3
+
z
3
−
3
x
y
z
will be:
0
4(a + b + c)
3abc
a + b + c
Validate
Solution:
👈: Video Solution
We know the identity
x
3
+
y
3
+
z
3
−
3
x
y
z
=
(
x
+
y
+
z
)
(
x
2
+
y
2
+
z
2
−
x
y
−
y
z
−
z
x
)
Now x = a - b
y = b - c
z = c - a
Adding these equation, we get:
x + y + z = a - b + b - c + c - a
x + y + z = 0
if x + y + z = 0
then
x
3
+
y
3
+
z
3
−
3
x
y
z
=
0
© examsnet.com
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