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

  • question_answer
    If \[\left( \mathbf{3a}+\mathbf{4b} \right)=\mathbf{16}\] and \[\mathbf{ab}=\mathbf{4}.\]Find the value of \[\left( \mathbf{9}{{\mathbf{a}}^{\mathbf{2}}}+\mathbf{16}{{\mathbf{b}}^{\mathbf{2}}} \right)\]

    A)  160  

    B)  100            

    C)  120                             

    D)  140

    Correct Answer: A

    Solution :

    (a): \[{{\left( 3a+4b \right)}^{2}}={{16}^{2}}\] \[\Rightarrow 9{{a}^{2}}+16{{b}^{2}}+24ab=256\] But, ab = 4 \[\Rightarrow 9{{a}^{2}}+16{{b}^{2}}+24ab=256\] \[\Rightarrow 9{{a}^{2}}+16{{b}^{2}}=160.\]


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