ICSE Class X Math 2016 Solved Paper

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Question : 33
Total: 57
If ‌
x
a
=‌
y
b
=‌
z
c
show that ‌
x3
a3
+‌
y3
b3
+‌
z3
c3
=‌
3xyz
abc
.
Solution:  
Given: ‌‌‌
x
a
=‌
y
b
=‌
z
c
=k
(say)
‌⇒‌‌x=ak,y=bk,z=ck
‌‌ L.H.S. ‌=‌
x3
a3
+‌
y3
b3
+‌
z3
c3

‌‌=‌
a3k3
a3
+‌
b3k3
b3
+‌
c3k3
c3

‌‌=k3+k3+k3=3k3
‌‌=3k⋅k⋅k
‌‌=3‌
x
a
‌
y
b
‌
z
c

(∵x=ak,y=bk,z=ck)
‌‌=‌
3xyz
abc
=‌ R.H.S. ‌
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