if each of a, b and c is a non zero number and a/b = b/c show that (a + b + c)(a - b + c) = a^2 + b^2 + c^2
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Answer:
Given,
a+b+c=0
or, a+b=−c
cubing both sides we get,
(a+b)
3
=−c
3
a
3
+b
3
+3ab(a+b)=−c
3
[∵(a+b)
3
=a
3
+3a
2
b+3ab
2
+b
3
]
a
3
+b
3
−3abc=−c
3
[Since a+b=−c]
a
3
+b
3
+c
3
=3abc.......(1).
Now,
bc
a
2
+
ac
b
2
+
ab
c
2
=
abc
a
3
+b
3
+c
3
=
abc
3abc
[Using (1)]
=3.
Step-by-step explanation:
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