SOLUTION: ab = ½, bc = ⅓, ac = 1/6, find (1/a²) + (1/b²) + (1/c²)

Question 1209563: ab = ½, bc = ⅓, ac = 1/6,
find (1/a²) + (1/b²) + (1/c²)

Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

I don't like manipulating fractions, so I'll do it this way to minimize such manipulation. Multiply the 1st equation by c, the 2nd by a and the 3rd by b So Multiply through by 6 Substitute 2a for b in ab=1/2, then get a, b, and c. --------------------------------------------------------------- Edwin

Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

Note to begin with that the expression we are to evaluate is , so we don't need to be concerned with positive or negative values of a, b, and c.

Given:
[1]
[2]
[3]

Multiply all three equations together to get

[4]

From [1] and [4], c=1/3, so 1/c^2=9.
From [2] and [4], a=1/2, so 1/a^2=4.
From [3] and [4], b=1, o 1/b^2=1.

And then

ANSWER:

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