document.write( "Question 1016895: if a,b are positive numbers such that a+b=1 , prove that a^2+b^2 >= 1/2 \n" ); document.write( "

Algebra.Com's Answer #633240 by robertb(5830) $\"\"$ $\"About$

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$\"a%5E2+%2B+b%5E2++=+a%5E2+%2B+%281-a%29%5E2+=+2a%5E2+-2a%2B1\"$
\n" ); document.write( "Now for any quadratic expression $\"Ax%5E2+%2BBx+%2B+C\"$ , the maximum or minimum value is $\"C-B%5E2%2F%284AC%29\"$ . In this case, A = 2 >0, and hence we have a minimum value.\r
\n" ); document.write( "\n" ); document.write( "The minimum value of $\"2a%5E2+-2a%2B1\"$ is then equal to $\"1-%28-2%29%5E2%2F%284%2A2%2A1%29+=+1+-+4%2F8+=+1%2F2\"$ .\r
\n" ); document.write( "\n" ); document.write( "This ends the solution. \n" ); document.write( "

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