document.write( "Question 1011723: t^2-k^2<6
\n" ); document.write( "t+k>4
\n" ); document.write( "t and k are positive in integers if t>k what is the value of t?
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Algebra.Com's Answer #627473 by rothauserc(4718) $\"\"$ $\"About$

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1) t^2 - k^2 < 6
\n" ); document.write( "2) t + k > 4
\n" ); document.write( "from inequality 1
\n" ); document.write( "(t+k)(t-k) < 6
\n" ); document.write( "t > k means (t-k) > 0, therefore
\n" ); document.write( "4 < t + k < 6 / (t - k)
\n" ); document.write( "4(t-k) < (t+k)(t-k) < 6
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\n" ); document.write( "first case
\n" ); document.write( "4 < t + k
\n" ); document.write( "4 - k < t
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\n" ); document.write( "second case
\n" ); document.write( "4(t-k) < 6
\n" ); document.write( "t -k < 1.5
\n" ); document.write( "t < k + 1.5
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\n" ); document.write( "we have
\n" ); document.write( "4 - k < t < k + 1.5
\n" ); document.write( "4 < t+k < 2k + 1.5
\n" ); document.write( "2k + 1.5 > 4
\n" ); document.write( "2k > 2.5
\n" ); document.write( "k > 5/4
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\n" ); document.write( "note that t and k are positive integers, therefore
\n" ); document.write( "k=2 and t=3
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\n" ); document.write( "check answer
\n" ); document.write( "inequality 1
\n" ); document.write( "3^2 - 2^2 < 6
\n" ); document.write( "5 < 6
\n" ); document.write( "inequality 2
\n" ); document.write( "3 + 2 > 4
\n" ); document.write( "5 > 4
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