Algebra


  1. If the sum of 
    a
      and its reciprocal is 1 and a ≠ 0, b ≠ 0, then the value of a3 + b3 is
    b










  1. View Hint View Answer Discuss in Forum

    According to question,

    a
    +
    b
    = 1
    aa

    ⇒ a2 + b2 = ab
    ⇒ a2 – ab + b2 = 0
    ∴ a3 + b3 = (a + b)( a2 – ab + b2 ) = 0

    Correct Option: C

    According to question,

    a
    +
    b
    = 1
    aa

    ⇒ a2 + b2 = ab
    ⇒ a2 – ab + b2 = 0
    ∴ a3 + b3 = (a + b)( a2 – ab + b2 ) = 0


  1. If a = √7 + 2√12 and b = √7 - 2√12 , then ( a3 + b3 ) is equal to









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    a = √7 + 2 × √4 × √3
    = √4 + 3 + 2 × 2 × √3
    = √( 2 + √3 )2 = 2 + √3
    ∴ b = √7 - 2√12 = 2 - √3
    ⇒ a + b = 2 + √3 + 2 - √3 = 4
    ab = (2 + √3)(2 - √3) = 1
    ∴ a3 + b3 = ( a + b )3 - 3ab(a + b)
    = 64 – 3 × 4 = 52

    Correct Option: D

    a = √7 + 2 × √4 × √3
    = √4 + 3 + 2 × 2 × √3
    = √( 2 + √3 )2 = 2 + √3
    ∴ b = √7 - 2√12 = 2 - √3
    ⇒ a + b = 2 + √3 + 2 - √3 = 4
    ab = (2 + √3)(2 - √3) = 1
    ∴ a3 + b3 = ( a + b )3 - 3ab(a + b)
    = 64 – 3 × 4 = 52



  1. If a = 11 and b = 9, then the value of
    a2 + b2 + ab
    is :
    a3 - b3









  1. View Hint View Answer Discuss in Forum

    a2 + ab + b2
    =
    a2 + ab + b2
    a3 - b3( a - b )( a2 + ab + b2 )

    =
    1

    a - b

    =
    1
    =
    1
    11 - 92

    Correct Option: A

    a2 + ab + b2
    =
    a2 + ab + b2
    a3 - b3( a - b )( a2 + ab + b2 )

    =
    1

    a - b

    =
    1
    =
    1
    11 - 92


  1. x +
    1
    x -
    1
    x2 +
    1
    - 1x2 +
    1
    + 1 is equal to
    xxx2x2









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    x +
    1
    x -
    1
    x2 +
    1
    - 1x2 +
    1
    + 1
    xxx2x2

    = x2 -
    1
    x2 +
    1
    2 - 1
    x2x2

    = x2 -
    1
    x4 +
    1
    + 1
    x2x4

    Required answer = x6 -
    1
    x6

    Correct Option: D

    x +
    1
    x -
    1
    x2 +
    1
    - 1x2 +
    1
    + 1
    xxx2x2

    = x2 -
    1
    x2 +
    1
    2 - 1
    x2x2

    = x2 -
    1
    x4 +
    1
    + 1
    x2x4

    Required answer = x6 -
    1
    x6



  1. If a = 4 . 36, b = 2.39 and c = 1.97, then the value of a3 - b3 - c3 – 3abc is









  1. View Hint View Answer Discuss in Forum

    Using Rule 21,
    Here, a – b – c = 4.36 – 2.39 – 1.97 = 0 ( ∴ a - b - c = 0)
    ∴ a3 - b3 - c3 = 3abc = 0
    ⇒ a3 - b3 - c3 - 3abc = 0

    Correct Option: C

    Using Rule 21,
    Here, a – b – c = 4.36 – 2.39 – 1.97 = 0 ( ∴ a - b - c = 0)
    ∴ a3 - b3 - c3 = 3abc = 0
    ⇒ a3 - b3 - c3 - 3abc = 0