Let’s consider a and r to be the first term and the common ratio of the G.P. respectively.
Given, a = 1
a3 = ar2 = r2
a5 = ar4 = r4
Then, from the question we have
r2 + r4 = 90
r4 + r2 – 90 = 0
\( r^2=\dfrac{-1+\sqrt{1+360}}{2}\)
= \( \dfrac{-1\pm\sqrt{1+360}}{2}\)
= \( \dfrac{-1\pm19}{2}\)
= -10 or 9
\( r\pm3\)
Answered by Pragya Singh | 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 \( \dfrac{81}{2}\).