Question

If 2,3^x-6,9÷2 are first three terms of gp Sum of all values of x is

Answer 1

Answer:

We have,

a,b,c are in A.P.

2b=a+c       ……. (1)

 

a,x,b are in G.P.

x  

2

=ab           …… (2)

b,y,c are in G.P.

y  

2

=bc         ……. (3)

 

From equation (1) and (2), we get

x  

2

=(2b−c)b

x  

2

=2b  

2

−bc

 

On putting the value of bc in above expression, we get

x  

2

=2b  

2

−y  

2

 

2b  

2

=x  

2

+y  

2

 

 

So, x  

2

,b  

2

,y  

2

 are in A.P.

 

Hence, provedWe have,

a,b,c are in A.P.

2b=a+c       ……. (1)

 

a,x,b are in G.P.

x  

2

=ab           …… (2)

b,y,c are in G.P.

y  

2

=bc         ……. (3)

 

From equation (1) and (2), we get

x  

2

=(2b−c)b

x  

2

=2b  

2

−bc

 

On putting the value of bc in above expression, we get

x  

2

=2b  

2

−y  

2

 

2b  

2

=x  

2

+y  

2

 

 

So, x  

2

,b  

2

,y  

2

 are in A.P.

 

Hence, proved.

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