The equation has a single solution $\alpha$ in the interval $[2.1, 2.2]$ .

By considering a suitable change of sign, show that $α\alpha$ lies between 2.1 and 2.2.

Show that the equation $Y^3 - 6Y + 3 = 0$ can be rearranged into the form

\sqrt{6 - \frac{3}{Y}}

Use the iterative formula

Y_{n+1} = \sqrt{6 - \frac{3}{Y_n}}

with $Y_1 = 2.1$ , to determine the values of $Y_2, Y_3$ and $Y_4$ , giving your answers to four decimal places.

Hence, deduce an interval of width 0.001 in which $α\alpha$ lies.

The equation has a single solution $\alpha$ in the interval $[2.1, 2.2]$ .

By considering a suitable change of sign, show that $α\alpha$ lies between 2.1 and 2.2.

Show that the equation $Y^3 - 6Y + 3 = 0$ can be rearranged into the form

\sqrt{6 - \frac{3}{Y}}

Use the iterative formula

Y_{n+1} = \sqrt{6 - \frac{3}{Y_n}}

with $Y_1 = 2.1$ , to determine the values of $Y_2, Y_3$ and $Y_4$ , giving your answers to four decimal places.

Hence, deduce an interval of width 0.001 in which $α\alpha$ lies.

1 Pure Mathematics

1 Pure Mathematics Questions