Just by looking, (a or b) = 2, and (a or b) = 6.Originally Posted bydgolverk

Let us use some Math.

Here is one way.

a +b = 8 ----(i)

ab = 12 -----(ii)

From (ii), a = 12/b

Substitute that into (i),

12/b +b = 8

Clear the fraction, multiply both sides by b,

12 +b^2 = 8b

b^2 -8b +12 = 0

(b-2)(b-6) = 0

b-2 = 0

b = 2

b-6 = 0

b = 6

So, b = 2 or 6 --------***

Then, a = 12/b = 6 or 2 ----------***

Hence, we have two sets of answers:

a=2, and b=6 -----(1)

a=6, and b=2 -----(2)

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When a=2 and b=6:

a -b = 2 -6 = -4 -----------------------------answer.

a^2 +b^2 = 2^2 +6^2 = 4 +36 = 40 ---------answer.

1/(a^2) +1/(b^2)

= 1/(2^2) +1/(6^2)

= 1/4 +1/36

= (9 +1)/36

= 10/36

= 5/18 ------------------answer.

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When a=6 and b=2:

a -b = 6 -2 = 4 -----------------------------answer.

a^2 +b^2 = 6^2 +2^2 = 36 +4 = 40 ---------answer.

1/(a^2) +1/(b^2)

= 1/(6^2) +1/(2^2)

= 1/36 +1/4

= (1 +9)/36

= 10/36

= 5/18 ------------------answer.