1. If 3a + 5b + 4c = 0, show that :
27a3 + 12563 + 64c3 = 180 abc.
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Explanation:
We know that
(a+b+c)
3
=(a
3
+b
3
+c
3
)+3[(a+b+c)(ab+ac+bc)−abc]
If (a+b+c)=0, then a
3
+b
3
+c
3
=3abc
Given, 3a+5b+4c=0
Here, a=3a, b=5b and c=4c
Now,
L.H.S =27a
3
+125b
3
+64c
3
=(3a)
3
+(5b)
3
+(4c)
3
=3(3a)(5b)(4c)
=180abc
=R.H.S
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