a By sketching a suitable pair of graphs, show that the equation 7 x 6 x 2 1 has exactly two real roots, and , where is a positive constant b Show that satisfies the equation c Write down an iterative formula based on the equation in part a Use this formula, with a suitable starting value, to find ...

a To show that the equation 7 x6 x2 1 has exactly two real roots and where is a positive constant we can sketch the graphs of the functions y 7 x6 and ...

a. By sketching a suitable pair of graphs, show that the equation 7 - x 6 =

Question:

a. By sketching a suitable pair of graphs, show that the equation 7 - x⁶= |x²- 1|has exactly two real roots, α and β, where α is a positive constant.
b. Show that α satisfies the equation

c. Write down an iterative formula based on the equation in part a. Use this formula, with a suitable starting value, to find the value of α correct to 3 significant figures. Give the result of each iteration to 5 significant figures.

b. Hence write down the value of β correct to 3 significant figures.

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