Question 1209307
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Let x and y be nonnegative real numbers.  
If x^2 + 5y^2 = 30, then find the maximum value of x^2 + y^2.
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From the given equation  

    x^2 + 5y^2 = 30,

express

    x^2 = 30 - 5y^2

and substitute it into another expression.  You will get

    x^2 + y^2 = (30-5y^2) + y^2 = 30 - 4y^2.


It has the maximum value of 30 when y = 0  (which is a non-negative real number).


<U>ANSWER</U>.  The requested maximum value of  x^2+y^2  is  30.
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Solved.