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tmua.me Extreme Set B Paper 1 · Q8

Paper 1Sequences & series

A real constant cc is to be chosen so that three distinct points common to the curves

y=2xandy=(x−c)2y=2^x\qquad\text{and}\qquad y=(x-c)^2

have xx-coordinates which, in increasing order, form an arithmetic progression.

Which of the following is possible for the common difference of this progression?

Alog⁡2(1+2)\log_2(1+\sqrt2)
Blog⁡23\log_2 3
Clog⁡2(2+2)\log_2(2+\sqrt2)
Dlog⁡2(3+22)\log_2(3+2\sqrt2)
Elog⁡2(17+122)\log_2(17+12\sqrt2)
FNo such choice of cc is possible

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