Question

proportional of a and cis b then prove that a, C,
(b) If b is the mean proportional of a and c, prove that the mean proportional of a? +62 and b? + c?
is ab + bc.
(c) If b is the mean proportional of a and c, prove that
ab + bc + ca
= abc.
a+b+c
3​

Answer 1

Answer:

please reply if you had understood .

Step-by-step explanation:

Since, b is  the mean proportional between a and c. So b2 = ac.

L.H.S. = a2 – b2 + c2/a-2 – b-2 + c-2  

= a2 – b2 + c2/1/a2 – 1/b2 + 1/c2

= (a2 – b2 + c2)/b2c2 – a2c2 + a2b2/a2b2c2

= a2b2c2 (a2 – b2 + c2)/b2c2 – b4 + a2b2

= b4 × b2(a2 – b2 + c2)/b2(c2 – b2 + a2)

b4 = R.H.S.

Hence proved.