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

  • question_answer
    If \[3x+4y=18\] and \[xy=6\], find the value of \[9{{x}^{2}}+16{{y}^{2}}\].

    A)  180                            

    B)  144                

    C)  324                

    D)         170    

    Correct Answer: A

    Solution :

    We have, \[3x+4y=18~\]       ?(i) \[xy=6~\]                                            ?(ii) Squaring both sides of (i), we get \[{{(3x)}^{2}}+{{(4y)}^{2}}+2\times 3x\times 4y={{(18)}^{2}}\] \[=9{{x}^{2}}+16{{y}^{2}}+24xy=324\] \[9{{x}^{2}}+16{{y}^{2}}+24(6)=324\]          (Using (ii)) \[9{{x}^{2}}+16{{y}^{2}}+144=324\] \[\Rightarrow 9{{x}^{2}}+16{{y}^{2}}=180\]


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