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8th Class Mathematics Algebraic Expressions Question Bank Algebraic Expressions and Identities

  • question_answer
    If \[3x-7y=10\] and \[xy=-1\], then the value of \[9{{x}^{2}}+49{{y}^{2}}\] is __.

    A)  58                              

    B)  142    

    C)  104                

    D)         -104   

    Correct Answer: A

    Solution :

    We have, \[3x-7y=10~~~~~~...(i)\] And \[xy=-1~~~~~~~~~~...(ii)\] Squaring both sides of (i), we get \[{{(3x)}^{2}}+{{(7y)}^{2}}-2\times 3x\times 7y={{10}^{2}}\] or \[9{{x}^{2}}+49{{y}^{2}}-42xy=100\] or \[9{{x}^{2}}+49{{y}^{2}}-42(-1)=100\]       (Using (i)) \[\therefore \] \[9{{x}^{2}}+49{{y}^{2}}=100-42=58\]


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