CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 9 – Sequences and Series Maths
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2 2
a b a b 4ab 36ab 4ab 32ab
a b 32 ab
4 2 ab ...... 2
Adding (1) and (2), we obtain
2 a 6 4 2
a
32 2
ab
ab
Substituting the value of a
b 6 ab 3 2 2 ab
b 3
2 2
a
b
ab
3
2 2 ab 3
2 2
3
2 2 ab 3 2 2
in (1), we obtain
Thus, the required ratio is
32 2 : 32 2
.
Question 29:
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the
numbers are
Solution 29:
A A G A G
It is given that A and G are A.M. and G.M. between two positive numbers.
Let these two positive numbers be a and b .
a
b
AM A
2
GM G ab
..... 1
.... 2
From (1) and (2), we obtain
a b 2 A ..... 3
ab
G
2
....... 4
Substituting the value of a and b
2 2
a b a b 4ab
,
We obtain
a b 2 4A 2 4G 2 4 A 2 G
2
from (3) and (4) in the identity
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