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

  • question_answer
    If \[\mathbf{a}+\mathbf{b}=\mathbf{7}\]and \[\mathbf{ab}=\mathbf{12}\] then what is the value of \[{{\mathbf{a}}^{\mathbf{2}}}-\mathbf{ab}-{{\mathbf{b}}^{\mathbf{2}}}\]

    A)  12                               

    B)  13             

    C)  14                               

    D)  \[-\]5

    Correct Answer: D

    Solution :

    (d): \[{{\left( a-b \right)}^{2}}={{\left( a+b \right)}^{2}}-4ab\] \[=49-48=1\Rightarrow a-b=1\]  \[a+b=7\] \[a-b=1\Rightarrow a=4,b=3\] \[{{a}^{2}}-ab-{{b}^{2}}\] \[=16-12-9=-5.\]


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