The value of a has to be determined given that 6a^-2 +
a^-1 = 2
Note that the exponent of a^-2 is twice that of
a^-1. It is possible to convert 6a^-2 + a^-1 = 2 into a quadratic
equation.
6a^-2 + a^-1 = 2
Let
x = a^-1.
6x^2 + x = 2
6x^2 +
x - 2 = 0
6x^2 + 4x - 3x - 2 =
0
2x(3x + 2) - 1(3x + 2)
=0
(2x - 1)(3x +2) = 0
x = 1/2
and x = -2/3
Now x = a^-1
a =
2 and a = -1.5
The equation 6a^-2 + a^-1 = 2 has solution a
= 2 and a = -1.5
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