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    Subject

    Quantitative Aptitude

    Topic

    Simplification

    If x = √6 + √5 then find the value of x3– (1/x)3=?

    ক)
    23
    খ)
    63√6
    গ)
    46√5
    ঘ)
    23√6
    ঙ)
    24√5

    Explanation

    x = √6 + √5 And 1x=16  +  5\frac{1}{x} = \frac{1}{{\sqrt 6 {\rm{\;}} + {\rm{\;}}\sqrt 5 }} =  6  −  5(6+  5)(6  −  5)= \;\frac{{\sqrt 6 \; - \;\sqrt 5 }}{{\left( {\sqrt 6 + \;\sqrt 5 } \right)\left( {\sqrt 6 \; - \;\sqrt 5 } \right)}} (Multiplying by 6−56−5\frac{{\sqrt 6 - \sqrt 5 }}{{\sqrt 6 - \sqrt 5 }} ) =6  −  56  −  5= \frac{{\sqrt 6 \; - \;\sqrt 5 }}{{6\; - \;5}} = √6 - √5 ∴ x – (1/x) = √6 + √5 - √6 + √5 = 2√5 ∴ x 3 – (1/x) 3 = [x – (1/x)] 3 + 3[x – (1/x)] = (2√5) 3 + 3 × 2√5 = 40√5 + 6√5 = 46√5

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