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 – b2 = 400
b2 – 50b + 400 = 0
b2 – 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) a3b and ab3
(iii) –8 and –2
Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).
Insert 5 geometric means between 16 and \( \dfrac{1}{4}\).