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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 ?
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) Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin
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)
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Askiitians Experts Badiuddin
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