document.write( "Question 517528: show that sqrt(c) + sqrt(c-1)=2 for some number c between 1 and 2 \n" ); document.write( "

Algebra.Com's Answer #344809 by richard1234(7193) $\"\"$ $\"About$

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and

are strictly increasing functions of c, and are defined for all

. In addition, they are continuous so it follows that

is continuous and strictly increasing on [1,2]. At c=1,

, and at c=2,

is larger than 2. By the intermediate value theorem there must be some value c within [1,2] such that

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and

are continuous because they satisfy the conditions for continuity: that they exist everywhere (on [1,2]), the limit as c goes to some number exists, and the limit is equal to the number evaluated at c.\r
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\n" ); document.write( "\n" ); document.write( "http://en.wikipedia.org/wiki/Continuous_function \n" ); document.write( "

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