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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
(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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