Question

Write mean proportional between a and c​

Answer 1

Answer:

There is ur answer......I am putting some digits to answer you clearly.....

Step-by-step explanation:

It is given that

b is the mean proportical that os geometric mean between a and c....

=b2 ac ....................................................(1)

And we have to prove

(ab + bc)

is the mean proportional between

(a2+b2) and (b2 + c2 )

that is we have to prove

(ab + bc) = ( a2+b2c2)2

Consider

LHS

(ab + bc)2

expanding using formula

LHS = a2ac(c)2+ 2a.ac.c

=a3ac3+2a2c2

Taking ac as common

LHS =ac(a2+c22ac)

LHS = ac( a+c)2....................................(2)

Now,

RHS (a2+2b2c2)

using equation (1)

Taking common term out

RHS =a (a+c) c(a+c)

RHS =ac(a+c2)......................................(3)

From eq 2 and 3

LHS=RHS

Therefore it is proved that

(ab+bc)

is the mean proportional between

( a2+b2 ) and ( b2+c2 )

Now u can see that the proportional between a and c b2 b2 ko kaat kar dekh loo...

I hope it will help you......plzzz mark my answer the brainlist answer.....