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colakumarfanta
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IMO Bcolakumarfanta wrote:IS a^2 + b^2 >= 1?
1. A + b >= 1
2.a^2 - b^2 >= 1
st 1:
a +b >=1
Plugging in numbers for(a,b)
case 1: {1/2, 1/2}.
a^2 + b^2 >= 1 --------NO
case 2:(1,1)
a^2 + b^2 >= 1 ---YES
Inconsistent answers.
Insufficient
st 2 : a^2 - b^2 >= 1
a^2 >= 1+b^2
substitute this value of a^2 in main equation:
a^2 + b^2
1+b^2 + b^2 >=1
try some plugging in numbers :
b =0 --> a= 1--> a^2 + b^2 >= 1 --YES
b= -2---> a=5--> a^2 + b^2 >= 1----yes
IMO B
