If m is a solution of x^2=2x-1, show that
i) m^3=3m-2
ii) m^4 - m^2=2m-2.
The question did not ask us to find the value of m. And I do not think the solution would ibe finding the value of m and substituting it back and do the LHS=RHS approach.
If m is a solution of x^2=2x-1, show that
i) m^3=3m-2
ii) m^4 - m^2=2m-2.
The question did not ask us to find the value of m. And I do not think the solution would ibe finding the value of m and substituting it back and do the LHS=RHS approach.
i) $\displaystyle m^2 = 2m - 1$.
Therefore:
$\displaystyle m^3 = 2m^2 - m$ ..... (1)
$\displaystyle 2m^2 = 4m - 2 \Rightarrow 2m^2 - m = 3m - 2$ .... (2)
Substitute (2) into (1) and it's blue sky all the way.
ii) Use a similar technique. You might need to use the result found in i).