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tmua.me Extreme Set C Paper 2 · Q2

Paper 2Algebra

For a real constant kk, the equation

2−∣x∣+3 2−∣x−2∣=k2^{-|x|}+3\,2^{-|x-2|}=k

has four distinct real solutions x1,x2,x3,x4x_1,x_2,x_3,x_4.

What is the value of

2x1+x2+x3+x4 ?2^{x_1+x_2+x_3+x_4}\,?
A43\dfrac43
B20821\dfrac{208}{21}
C527\dfrac{52}{7}
D1616
E2087\dfrac{208}{7}
F2083\dfrac{208}{3}

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