Linearly quadratic
Given: x + y + z = 4
x 2 + y 2 + z 2 = 6
for real numbers x , y and z . If the exhaustive range of values that x can take is given by [ α , β ] , find 6 ( α + β ) .
The answer is 16.
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2 solutions
Thanks for the solution!
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If you are going to be online for 2-3 more minutes , can you just check out Hangouts ? I have asked you a question here .
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i will, but my net is slow.
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@Raghav Vaidyanathan – Question
What do you mean by
expected value
w.r.t the question above ?
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@A Former Brilliant Member – For some series.. the value of the required term be x . let the probability that this series occurs be p , the contribution of this series to the expected value will be p x . The expected value is the sum of these contributions over all possible series. It is the "average value" of the required term .
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@Raghav Vaidyanathan – Thanks , I got it now . But I'm still not getting how to solve your question , but I'll manage it .
@Raghav Vaidyanathan – So are you practicing Physics on B'ant ,for now ? U have reshared so many Physics questions .
Hmmm , good to see two quick solutions from two genii .
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I know you wouldn't like me asking this but how's your mains Azhaghu
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Not as well as you . I am getting less than 250 , while your's must be greater than 300 .
I'm practicing for BITSAT so I can increase my speed , which will help me for the exams yet to come .
You might have seen that my points have increased a lot during these 3 days , the reason for it is same .
Just so you know , my first name's Roopesh . Azhaghu is part of my surname .But I don't mind which ever you find it comfortable to use .
Hint : Use the inequality (in terms of x ):
( 2 A + B ) 2 ≤ 2 A 2 + B 2
Thank you for the help!
Applying Cauchy-Schwarz inequality we have :
2 ( y 2 + z 2 ) ≥ ( y + z ) 2
Put the values from the given equations to get :
2 ( 6 − x 2 ) ≥ ( 4 − x ) 2
Simplifying we have :
3 x 2 − 8 x + 4 ≤ 0