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tmua.me Extreme Set C Paper 1 · Q5

Paper 1Algebra

For nonzero real xx, define

f(x)=x2+1x2,g(x)=x2−3x.f(x)=x^2+\frac1{x^2},\qquad g(x)=x^2-3x.

What is the sum of the squares of all the distinct nonzero real numbers aa for which there is a nonzero real number b≠ab\ne a satisfying

f(a)=f(b)andg(a)=g(b) ?f(a)=f(b)\qquad\text{and}\qquad g(a)=g(b)\,?
A44
B77
C99
D1111
E1414
F1818

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