document.write( "Question 1209307: Let x and y be nonnegative real numbers. If x^2 + 5y^2 = 30, then find the maximum value of x^2 + y^2. \n" ); document.write( "

Algebra.Com's Answer #848211 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "Let x and y be nonnegative real numbers.
\n" ); document.write( "If x^2 + 5y^2 = 30, then find the maximum value of x^2 + y^2.
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document.write( "From the given equation  \r\n" );
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document.write( "    x^2 + 5y^2 = 30,\r\n" );
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document.write( "express\r\n" );
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document.write( "    x^2 = 30 - 5y^2\r\n" );
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document.write( "and substitute it into another expression.  You will get\r\n" );
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document.write( "    x^2 + y^2 = (30-5y^2) + y^2 = 30 - 4y^2.\r\n" );
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document.write( "It has the maximum value of 30 when y = 0  (which is a non-negative real number).\r\n" );
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document.write( "ANSWER.  The requested maximum value of  x^2+y^2  is  30.\r\n" );
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