CBSE Class 12-science Answered
Consider the equation
. Choose the CORRECT option(s).
The sum of all solutions = 0<
The number of solutions = 2<
The number of solution = 1<
The sum of squares of all solutions = 1<
![](data:image/.png;base64,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)
Asked by harshsharma2531 | 09 Aug, 2020, 09:28: AM
To find solutions of the equation tan-1(x-1/x-2) + tan-1(x+1/x+2) = pi/4
![tan to the power of negative 1 end exponent open parentheses fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction close parentheses plus tan to the power of negative 1 end exponent open parentheses fraction numerator straight x plus 1 over denominator straight x plus 2 end fraction close parentheses equals straight pi over 4
rightwards double arrow tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction plus fraction numerator straight x plus 1 over denominator straight x plus 2 end fraction end style over denominator 1 minus begin display style fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction end style cross times begin display style fraction numerator straight x plus 1 over denominator straight x plus 2 end fraction end style end fraction close parentheses equals straight pi over 4
rightwards double arrow tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses straight x minus 1 close parentheses open parentheses straight x plus 2 close parentheses plus open parentheses straight x plus 1 close parentheses open parentheses straight x minus 2 close parentheses end style over denominator straight x squared minus 4 minus open parentheses straight x squared minus 1 close parentheses end fraction close parentheses equals straight pi over 4
rightwards double arrow tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style straight x squared plus straight x minus 2 plus straight x squared minus straight x minus 2 end style over denominator straight x squared minus 4 minus open parentheses straight x squared minus 1 close parentheses end fraction close parentheses equals straight pi over 4
rightwards double arrow tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style 2 straight x squared minus 4 end style over denominator negative 3 end fraction close parentheses equals straight pi over 4
rightwards double arrow fraction numerator begin display style 2 straight x squared minus 4 end style over denominator negative 3 end fraction equals tan straight pi over 4 equals 1
rightwards double arrow fraction numerator 2 straight x squared minus 4 over denominator negative 3 end fraction equals 1
rightwards double arrow 2 straight x squared minus 4 equals negative 3
rightwards double arrow 2 straight x squared equals 1
rightwards double arrow straight x equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction
Sum space of space all space solutions equals fraction numerator 1 over denominator square root of 2 end fraction minus fraction numerator 1 over denominator square root of 2 end fraction equals 0
Number space of space solutions space equals space 2
Sum space of space squares space of space all space solutions equals 1 half plus 1 half equals 1](https://images.topperlearning.com/topper/tinymce/cache/d9077909c4b20695772339216818b0f7.png)
Answered by Renu Varma | 09 Aug, 2020, 16:32: PM
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