NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 9

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1. If are in G.P, prove that are in G.P.

Answer:

It is given that are in G.P.

……………………………eq (1)

……………………………eq (2)

…………………………… eq (3)

It has to be proved that are in G.P.

i.e

Consider L.H.S.

[Using (1) and (2)]

[Using (3)]

Thus, are in G.P.

2. If a and b are the roots of are roots of ,where , form a G.P.

Prove that .

Answer:

It is given that a and b are the roots of

…………………………eq (1)

Also, are the roots of

……………………… eq (2)

It is given that are in G.P.

Consider From (1) and (2), we obtain

On dividing, we obtain

When

When

Case I:

When ,

i.e.,

Case II

When ,

i.e.,

Thus, in both the cases, we obtain