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Maths Made Easy TMUA Paper 1 · Q1

Paper 1Algebra

Real numbers xx and yy satisfy

x2+xy+y2=7.x^2+xy+y^2=7.

Find the complete set of values that x+yx+y can take.

A−23≤x+y≤23-2\sqrt3\le x+y\le2\sqrt3
B−7≤x+y≤7-\sqrt7\le x+y\le\sqrt7
C−2213≤x+y≤2213-\frac{2\sqrt{21}}3\le x+y\le\frac{2\sqrt{21}}3
Dx+yx+y can be any real number
E−21≤x+y≤21-\sqrt{21}\le x+y\le\sqrt{21}

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