tmua.me Tau Paper 1 · Question 6

tmua.me papers

tmua.me Tau Paper 1 · Q6

Paper 1TrigonometryAlgebra

For a real number $k$ , the equation

64\cos^4x-100\cos^2x-9=64k\cos x

has exactly six distinct solutions $x_1,\ldots,x_6$ in $0\le x<2\pi$ .

As $k$ varies over all values for which this is true, what is the least possible value of

\sum_{j=1}^{6}\left(9\cos^2x_j-2\cos^4x_j\right)?

\dfrac{441}{32}

\dfrac{455}{32}

\dfrac{455}{64}

\dfrac{1103}{32}

\dfrac{697}{32}

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.