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Grade 11Algebra

the sum of squares of three distinct real numbers which form an increasing GP is S^2(common ratio r) if the sum of numbers is tS,then
1.If r=3 then t^2 cannot lie in
A.[1/3,1] B.(1,2) C.[1/3,3] D.(1,3)
2.if t^2=2 then the value of common ratio r is greater than
A. 9 B. 4 C. 2 D. 3

Profile image of Tushar
10 Years agoGrade 11
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1 Answer

Profile image of Vikas TU
10 Years ago
a,b,c be in G.P.
then,
b/a = c/b = r
and 
condtns. given are:

a^2 + b^2 + c^22 = S^2
and
a + b + c = tS
 
  1. if r = 3
then
b = 3a and c = 9a
therefore the eqn.s becomes:
 
13a = tS 
and 
91a^2 = S^2
dividing them it comes,
t = 13/root91
or
t^2 = 169/91 which is approx.  ====> 1 point something
that satiffies hence the B,C and D options excluding A.