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4x+sqrt(2x)=1

Source: 1959 AHSME Problem 38

August 14, 2013
AMC

Problem Statement

If 4x+2x=14x+\sqrt{2x}=1, then xx: <spanclass=′latex−bold′>(A)</span> is an integer<spanclass=′latex−bold′>(B)</span> is fractional<spanclass=′latex−bold′>(C)</span> is irrational<spanclass=′latex−bold′>(D)</span> is imaginary<spanclass=′latex−bold′>(E)</span> may have two different values <span class='latex-bold'>(A)</span>\ \text{is an integer} \qquad<span class='latex-bold'>(B)</span>\ \text{is fractional}\qquad<span class='latex-bold'>(C)</span>\ \text{is irrational}\qquad<span class='latex-bold'>(D)</span>\ \text{is imaginary}\qquad<span class='latex-bold'>(E)</span>\ \text{may have two different values}
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