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THE SUM OF SQUARES OF 3 DISTINCT REAL NUMBERS WHICH ARE IN G.P IS S 2 . IF THEIR SUM IS :- aS THEN a 2 LIES IN ?

THE SUM OF SQUARES OF 3 DISTINCT REAL NUMBERS WHICH ARE IN G.P IS S2 .IF THEIR SUM IS :-   aS  THEN a2 LIES IN      ?

Grade:

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear rahul

let b,br,br2 are  3 number

 

so s2= (b)2 +(br)2 +(br2)2    ..............1

 and as= b +br +br2    ..................2

square 2 eqation and divide it by equation 1

 a2 =(b +br +br2 )2/((b)2 +(br)2 +(br2)2 )

      =(1 +r +r2 )2/( 1+r2 +r4 )

      =(1 +r +r2 )/(1 -r +r2 )

 rearrange

r2 (a2-1) -r(a2+1) +(a2-1)=0

discrimnent must be greter than zero

 

(a2+1)2-4(a2-1)2>=0

or

(3a2-1)(3-a2)>=0

or

(a-√3)(a+√3)(a-1/3)(a+1/3)<=0

 

find a from this enequality

reject those value of a for which r=0 or r=1(since numbers are in gp)


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Regards,
Askiitians Experts
Badiuddin

 

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