saptarshikuar2003's blog

one Maths Doubt!!!
By saptarshikuar2003, history, 7 hours ago, In English

if a1+a2+a3+a4>b1+b2+b3+b4 then

is it right to say that p.a1+q.a2+r.a3+s.a4>p.b1+q.b2+r.b3+s.b4?????

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6 hours ago, # |
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No we can't say that

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6 hours ago, # |
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No, even if $$$p, q, r, s \ge 0$$$ you can't say for sure, counter-example: $$$a_1 = 5, a_2 = 5, a_3 = 3, a_4 = 5$$$ & $$$b_1 = 4, b_2 = 4, b_3 = 5, b_4 = 4$$$ then with $$$p = 1, q = 1, r = 2, s = 1$$$ the inequality does not hold.

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    6 hours ago, # ^ |
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    will it work for a situation like p>q>r>s????

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      6 hours ago, # ^ |
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      No, just permute sequence a and sequence b according to the coefficient sequence and you will get a counter-case.

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        6 hours ago, # ^ |
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        please give a case........

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          6 hours ago, # ^ |
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          it depends upon the sequence of numbers you are taking on both sides for example as per you condition let p = 4 , q = 3, r = 2 , s = 1 and left side sequence = {5,4,3,2} (sum = 14) and right side sequence = {9 , 1 , 1 , 1} (sum 12) so left side after multiplication = 40 and right side = 42.. it became large due to multiplying p * 9 which is 36. so you see it depends on the sequence you are considering.

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