if a,b,c are in continued proportion, prove that a^4+a^2^b^2 +b^4/b^4+b^2c^2+c^4=a^2/c^2
Answers
Answered by
6
Answer:
ANSWER
Here
b
a
=
c
b
∴b
2
=ac
i)LHS=
b
2
+bc+c
2
a
2
+ab+b
2
=
ac+bc+c
2
a
2
+ab+ac
[Putting b
2
=ac]
=
c(a+b+c)
a(a+b+c)
=
c
a
=RHS
ii)LHS=
b
4
+b
2
c
2
+c
4
a
4
+a
2
b
2
+b
4
=
(ac)
2
+b
2
c
2
+c
4
a
4
+a
2
b
2
+(ac)
2
=
a
2
c
2
+b
2
c
2
+c
4
a
4
+a
2
b
2
+a
2
c
2
=
c
2
(a
2
+b
2
+c
2
)
a
2
(a
2
+b
2
+c
2
)
=
c
2
a
2
=RHS
Similar questions