Question 1087364
<pre><b><font size = 5> 

if a^2 + 1 = a find the value of a^3.

    a² + 1 = a

a² - a + 1 = 0

We recognize the left side as one of the factors in
the factorization of the sum of two cubes 

a³ + 1 = (a + 1)(a² - a + 1) 

So we multiply both sides by (a + 1)

(a + 1)(a² - a + 1) = 0(a + 1)

             a³ + 1 = 0
                 
                 a³ = -1

                

Edwin</pre></b></font>