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    ...with these values of a and b, use the result (1 + 2x)^0.5 ≈ (1 + ax)/(1 + bx), with x = -0.01, to obtain an approximation of root 2, in the form p/q.

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    i obtained a and b by expanding and equating the left hand side of the equation above. but now, how does letting x = -0.01 help me get to 2^0.5 ?
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    (1+2x)^.5

    with x as -0.01
    =(0.98)^.5

    =(2*0.49)^.5

    =0.49^.5(2)^.5

    =(0.7)*(2)^.5


    (2)^.5=(1 - 0.01a)/0.7(1 - 0.01b)

    ??? is this right im not too sure myself
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    1-.02 = 49/50

    √(49/50) = 7/ √50 = 7/ 5√2 multiplying by √2 = 7√2 /10

    is the relation you may be looking for, recognize a similar question.

    edit: with the binomial approximation does it ask for a certain degree of accuracy i.e. what power of x are you going up to?
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    (Original post by Infinity_Kev)
    (1+2x)^.5

    with x as -0.01
    =(0.98)^.5

    =(2*0.49)^.5

    =0.49^.5(2)^.5

    =(1/7)*(2)^.5


    (2)^.5=(1 - 0.01a)/7(1 - 0.01b)

    ??? is this right im not too sure myself
    i presume this line should be 0.7√2? i get the idea, thanks.
 
 
 
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