+1242 Find all the values of a for which the equations \(\begin{align*} x^2 + ax + 1 &= 0, \\ x^2 - x - a &= 0 \end{align*}\)have a common real root. Enter all the possible values, separated by commas.
+128475 x^2 + ax + 1 = x^2 - x - a
ax + 1 = -x - a
ax + x = -1 - a
x(1 + a) = - ( 1 + a)
x = - (1 + a)
_______
(1 + a)
x = - 1 is the common root [if a not equal to -1 ]
Therefore using the first function
(-1)^2 + a(-1) + 1 = 0
1 - a + 1 = 0
2 - a = 0
a = 2
And using the second function as a check
(-1)^2 - (-1) - 2 = 0 ???
1 + 1 - 2 = 0
2 - 2 = 0 true
