document.write( "Question 765752: I need help help help\r
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\n" ); document.write( "\n" ); document.write( "∀x, u ∈ R ∃α,β ∈ [0, 1] such that (αx+βu)^3=x^3+u^3\r
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Algebra.Com's Answer #466391 by tommyt3rd(5050)\"\" \"About 
You can put this solution on YOUR website!
for convenience we use a=alpha, b=beta\r
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\n" ); document.write( "\n" ); document.write( "so we need \r
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\n" ); document.write( "\n" ); document.write( "(ax)^3=x^3
\n" ); document.write( "(bu)^3=u^3\r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( "3(ax)^2(bu)+3(ax)(bu)^2=0\r
\n" ); document.write( "\n" ); document.write( "all are possible if a,b,x,u = 0\r
\n" ); document.write( "\n" ); document.write( "another solution is a=b=1, x=-u\r
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\n" ); document.write( "\n" ); document.write( "I'm not positive, but I think this exhausts the real solutions\r
\n" ); document.write( "\n" ); document.write( ":) \n" ); document.write( "
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