document.write( "Question 1209563: ab = ½, bc = ⅓, ac = 1/6,
\n" ); document.write( "find (1/a²) + (1/b²) + (1/c²)
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Algebra.Com's Answer #849527 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Note to begin with that the expression we are to evaluate is $\"1%2Fa%5E2%2B1%2Fb%5E2%2B1%2Fc%5E2\"$ , so we don't need to be concerned with positive or negative values of a, b, and c.

\n" ); document.write( "Given:
\n" ); document.write( "[1] $\"ab=1%2F2\"$
\n" ); document.write( "[2] $\"bc=1%2F3\"$
\n" ); document.write( "[3] $\"ac=1%2F6\"$

\n" ); document.write( "Multiply all three equations together to get

\n" ); document.write( " $\"%28abc%29%5E2=1%2F36\"$
\n" ); document.write( "[4] $\"abc=1%2F6\"$

\n" ); document.write( "From [1] and [4], c=1/3, so 1/c^2=9.
\n" ); document.write( "From [2] and [4], a=1/2, so 1/a^2=4.
\n" ); document.write( "From [3] and [4], b=1, o 1/b^2=1.

\n" ); document.write( "And then

\n" ); document.write( "ANSWER: $\"1%2Fa%5E2%2B1%2Fb%5E2=1%2Fc%5E2=1%2B4%2B9=14\"$

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