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If sqrt(8-2sqrt(12))=sqrt(x)-sqrt(y) the...

If `sqrt(8-2sqrt(12))=sqrt(x)-sqrt(y)` then find `log_x 216 + log_y 128`

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Knowledge Check

  • If y=sqrt(x)^(sqrt(x)^(sqrt(x)^(sqrtx....oo))) , then (2-y log x)(dy)/(dx)=x

    A
    `xy^2 `
    B
    `(y^2)/(x)`
    C
    `y^2`
    D
    None

  • If y=log(sqrt(x) + sqrt(x-a)) , then (dy)/(dx) is

    A
    `1/(sqrt(x) + sqrt(x-a))`
    B
    `1/(2sqrt(x) sqrt(x-a))`
    C
    `1/(sqrt(x) sqrt(x-a))`
    D
    `1/(2(sqrt(x)+ sqrt(x-a)))`

  • If x-(2)/(sqrt(10)-sqrt(8)),y-(2)/(sqrt(10)+2sqrt(2)) , then (x-y)^(2) =

    A
    `4sqrt(2)`
    B
    32
    C
    `8sqrt(2)`
    D
    64

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