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 ?

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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