document.write( "Question 1196149: Find the exact value of x for which 4cosh(x) - e^-(x) = 3
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Algebra.Com's Answer #828870 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "(a) Find the exact value of x for which 4cosh(x) - e^-(x) = 3\r
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\n" ); document.write( "\n" ); document.write( "(b) Find the exact value of cosh^-¹(3) - sinh^-1(2)
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\n" ); document.write( "\n" ); document.write( " There are two problems in the post, which is prohibited by the rules of the forum.\r
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\n" ); document.write( "\n" ); document.write( " So, I will solve part (a) ONLY, in order for do not transform my response into a mess.\r
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document.write( "By the definition,  cosh(x) = .\r\n" );
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document.write( "So, I will introduce new variable  t = .  \r\n" );
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document.write( "Then the equation takes the form\r\n" );
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document.write( "     -  = 3.\r\n" );
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document.write( "Simplify it step by step\r\n" );
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document.write( "     -  = 3\r\n" );
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document.write( "    2t +  = 3\r\n" );
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document.write( "    2t^2 + 1 = 3t\r\n" );
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document.write( "    2t^2 - 3t + 1 = 0.\r\n" );
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document.write( "Apply the quadratic formula.  It will give two roots:  t = 1  and  t = .\r\n" );
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document.write( "If t = 1,  then   = 1  and  x = 0.\r\n" );
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document.write( "If t = ,  then   =   implies  x =  = -ln(2).\r\n" );
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document.write( "Thus part (a) has two solutions  x = 0  and  x = -ln(2).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Part (a) is just solved.\r
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\n" ); document.write( "\n" ); document.write( "Please do not submit more then one problem per post.\r
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\n" ); document.write( "\n" ); document.write( "Post the problems separately.\r
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