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(2 + sqrt5)/(2 - sqrt5)...

`(2 + sqrt5)/(2 - sqrt5)`

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The correct Answer is:
irrational
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The modulus of the complex number ((2+i sqrt(5))/(2-i sqrt(5)))^(10)+((2-i sqrt(5))/(2+i sqrt(5)))^(10) is equal to

Rationalize the denominator of (2+sqrt(5))/(2-sqrt(5))

Knowledge Check

  • If a = ( sqrt5 + 2)/( sqrt5 -2) and b = (sqrt5 - 2)/( sqrt5 + 2) then the value of a + b is

    A
    `4 sqrt5`
    B
    `18`
    C
    `-4 sqrt5`
    D
    `-18`

  • If (3+2sqrt(5))/(4-2sqrt(5))=p+qsqrt(5) where p and q are rational numbers, then values of p and q respectively are

    A
    `8,-7//2`
    B
    `-8,-7//2`
    C
    `+4,+7`
    D
    `-4,-7`

    • Similar Questions

    Explore conceptually related problems

    If a=(2+sqrt(5))/(2-sqrt(5)) and b=(2-sqrt(5))/(2+sqrt(5)) then find value of a+b and b=(2-sqrt(5))/(2+sqrt(5)) then find

    If a=(2-sqrt(5))/(2+sqrt(5)) and b=(2+sqrt(5))/(2-sqrt(5)), find a^(2)-b^(2)

    If a=2-sqrt(5) and b=(2+sqrt(5))/(2-sqrt(5)) find a^(2)-b^(2)

    In a ABC, if tan A:tan B:tan C=3:4:5 then the value of sin A sin B sin C is equal to (a) (2)/(sqrt(5)) (b) (2sqrt(5))/(7)(2sqrt(5))/(9) (d) (2)/(3sqrt(5))

    if x+ysqrt5=((2sqrt5)-1)/((2sqrt5)+1) then find x and y

    Which of the following statement(s) is/are TRUE? I. 2/(3 sqrt5) II. 3/(2 sqrt5)<2/(3 sqrt3)<7/(4 sqrt5)

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