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tmua.me Medium Set C Paper 1 · Q15

Paper 1Algebra

For which values of the real constant aa does

x2+1x2−2a(x+1x)+6a−3≥0x^2+\frac{1}{x^2}-2a\left(x+\frac{1}{x}\right)+6a-3\geq0

hold for every positive real number xx?

Aa≥12a\geq\dfrac12
B1≤a≤51\leq a\leq5
C12≤a≤2\dfrac12\leq a\leq2
D12≤a≤5\dfrac12\leq a\leq5
E0≤a≤50\leq a\leq5
F12<a<5\dfrac12<a<5

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