Given: A.M = 25, G.M = 20.

G.M = \( \sqrt{ab}\)

A.M = \( \dfrac{(a+b)}{2}\)

So,

\( \sqrt{ab}\) = 20 ……. (1)

\( \dfrac{(a+b)}{2}\) = 25……. (2)

a + b = 50

a = 50 – b

Putting the value of ‘a’ in equation (1), we get,

\( \sqrt{(50-b)b}= 20\)

50b – b^{2} = 400

b^{2} – 50b + 400 = 0

b^{2} – 40b – 10b + 400 = 0

b(b – 40) – 10(b – 40) = 0

b = 40 or b = 10

If b = 40 then a = 10

If b = 10 then a = 40

The numbers are 10 and 40.

Answered by Aaryan | 1 year agoConstruct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Find the geometric means of the following pairs of numbers:

**(i) **2 and 8

**(ii) **a^{3}b and ab^{3}

**(iii) **–8 and –2

Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).

Insert 5 geometric means between 16 and \( \dfrac{1}{4}\).