if b is the mean proportional of a and c
a^+b^/ab=a+c/b
Answers
Answered by
3
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
Step-by-step explanation:
hope it's helpful to you M'lady.
Similar questions