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    Question


    If is:

    A.

    1

    B.

    -1

    C.

    0

    D.

    2

    Correct option is A

    Given:

    A=582252462372,B=262152562152A = \frac{58^2 - 25^2}{46^2 - 37^2}, \quad B = \frac{26^2 - 15^2}{56^2 - 15^2}​​

    Formula Used:

    a2b2=(a+b)(ab)a^2 - b^2 = (a + b)(a - b)​​

    Solution:

    A=582252462372A=83×3383×9=113B=262152562152B=41×1171×41=11711B20A =71116011 =1111=1A = \frac{58^2 - 25^2}{46^2 - 37^2} \\A = \frac{83 \times 33}{83 \times 9} = \frac{11}{3} \\B = \frac{26^2 - 15^2}{56^2 - 15^2} \\B = \frac{41 \times 11}{71 \times 41} = \frac{11}{71} \\\frac{1}{B} - \frac{20}{A}\\ \ \\= \frac{71}{11} - \frac{60}{11} \\ \ \\= \frac{11}{11} = 1​​

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