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If a+ib = (x+i)^(2)/(2x^(2)+1), prove th...

If `a+ib = (x+i)^(2)/(2x^(2)+1)`, prove that `a^(2) + b^(2) = (x^(2)+1)^(2)/(2x^(2) + 1)^(2)`

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Knowledge Check

  • (2x^(2)-1)/((x-1)(2x^(2)+5x+2))=

    A
    `1/(9(x-1))+7/(9(x+2))+2/(9(2x+1))`
    B
    `1/(9(x+1))+7/(9(x-2))-2/(9(2x-1))`
    C
    `1/(9(x-1))-7/(9(x-2))+2/(9(2x+1))`
    D
    `1/(9(x-1))-7/(9(x+2))-2/(9(2x-1))`

  • int (1)/((x^(2)+a^(2))(x^(2)+b^(2)))dx=

    A
    `(1)/(b^(2)+a^(2))[(1)/(2)"Tan"^(-1)(x)/(a)-(1)/(b)"Tan"^(-1)(x)/(b)]+c`
    B
    `(1)/(b^(2)-a^(2))[(1)/(a)"Tan"^(-1)(x)/(a)+(1)/(b)"Tan"^(-1)(x)/(b)]+c`
    C
    `(1)/(b^(2)-a^(2))[(1)/(a)"Tan"^(-1)(x)/(a)-(1)/(b)"Tan"^(-1)(x)/(b)]+c`
    D
    none

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