If b is the mean proportion of a and C then prove that a²+b²/ab =a+C/b
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Answer:
It is given that
b is the mean proportional between a and c
We can write it as
b
2
=a×c
b
2
=ac⋯⋯(1)
We have to prove that a,c,a
2
+b
2
and b
2
+c
2
are in proportion
That is we have to prove
c
a
=
(b
2
+c
2
)
(a
2
+b
2
)
Consider, RHS=
(b
2
+c
2
)
(a
2
+b
2
)
=
ac+c
2
a
2
+ac
⋯⋯[from (1)]
=
c(a+c)
a(a+c)
=
c
a
=LHS
∴LHS=RHS
So, it is proved that a,c,a
2
+b
2
and b
2
+c
2
are in proportion
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