Answer:
79
Explanation:
To find the value of a^2 + 1/a^2, we need to manipulate the given equation to obtain the expression in terms of a^2.
We know that a + 1/a = 9.
To find a^2 + 1/a^2, we can square the given equation:
(a + 1/a)^2 = 9^2
Expanding the left side of the equation:
a^2 + 2(a)(1/a) + (1/a)^2 = 81
Simplifying:
a^2 + 2 + 1/a^2 = 81
Next, subtract 2 from both sides of the equation:
a^2 + 1/a^2 = 81 - 2
a^2 + 1/a^2 = 79
Therefore, the value of a^2 + 1/a^2 is 79.