Mathematics 9709 · AS & A Level · Numerical solution of equations

Numerical solution of equations — practice question

The curve with equation $y = \frac{6}{x^2}$ meets the line $y = x + 1$ at the point $P$.
(i)[2]

Verify by calculation that the $x$-coordinate of $P$ is between $1.4$ and $1.6$.

(ii)[2]

Show that the $x$-coordinate of $P$ satisfies the equation $x = \sqrt{\left(\frac{6}{x + 1}\right)}$.

(iii)[3]

Apply the iterative formula $x_{n+1} = \sqrt{\left(\frac{6}{x_n + 1}\right)}$ with starting value $x_1 = 1.5$ to find the $x$-coordinate of $P$ correct to 2 decimal places. Record each iterate to 4 decimal places.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Look at the sign of $\frac{6}{x^2}-x-1$ when $x=1.4$ and $x=1.6$, or an equivalent approach” …

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