Algebra


  1. If  
    x
    =
    y
    =
    z
      , then
    b + cc + aa + b









  1. View Hint View Answer Discuss in Forum

    x
    =
    y
    b + cb + a

    =
    x - y
    =
    x - y
    ;
    y
    =
    z
    b + c - c -ab - ac + aa + b

    =
    y - z
    =
    y - z
    ;
    z
    =
    x
    c + a - a - bc - ba + bb + c

    =
    z - x
    =
    z - x
    a + b - b - ca - c

    x - y
    =
    y - z
    =
    z - x
    b - ac - ba - c

    Correct Option: A

    x
    =
    y
    b + cb + a

    =
    x - y
    =
    x - y
    ;
    y
    =
    z
    b + c - c -ab - ac + aa + b

    =
    y - z
    =
    y - z
    ;
    z
    =
    x
    c + a - a - bc - ba + bb + c

    =
    z - x
    =
    z - x
    a + b - b - ca - c

    x - y
    =
    y - z
    =
    z - x
    b - ac - ba - c


  1. If   x = 3 + 2√2 and xy = 1, then the value of
    x2 + 3xy + y2
      is
    x2 − 3xy + y2









  1. View Hint View Answer Discuss in Forum

    x = 3 + 2√2
    ⇒ xy = 1

    ⇒ y =
    1
    =
    1
    ×
    3 - 2√2
    3 + 2√23 + 2√23 - 2√2

    =
    3 - 2√2
    = 3 - 2√2
    9 - 8

    ∴ x + y
    = 3 + 2√2 + 3 - 2√2 = 6
    x² + 3xy + y²
    =
    (x + y)² + xy
    x² - 3xy + y²(x - y)² - 5xy

    =
    36 + 1
    =
    37
    36 - 531

    Correct Option: D

    x = 3 + 2√2
    ⇒ xy = 1

    ⇒ y =
    1
    =
    1
    ×
    3 - 2√2
    3 + 2√23 + 2√23 - 2√2

    =
    3 - 2√2
    = 3 - 2√2
    9 - 8

    ∴ x + y
    = 3 + 2√2 + 3 - 2√2 = 6
    x² + 3xy + y²
    =
    (x + y)² + xy
    x² - 3xy + y²(x - y)² - 5xy

    =
    36 + 1
    =
    37
    36 - 531



  1. If   p + q = 10 and pq = 5, then the numerical value of
    p
    +
    q
    will be
    qp









  1. View Hint View Answer Discuss in Forum

    p
    +
    q
    =
    p² + q²
    pqpq

    =
    (p + q) - 2pq
    pq

    =
    100 - 2 × 5
    =
    90
    = 18
    55

    Correct Option: D

    p
    +
    q
    =
    p² + q²
    pqpq

    =
    (p + q) - 2pq
    pq

    =
    100 - 2 × 5
    =
    90
    = 18
    55


  1. If   n = 7 + 4 √3, then the value of n +
    1
    is :
    n









  1. View Hint View Answer Discuss in Forum

    n = 7 + 4√3 = 7 + 2 × 2 × √3
    = 4 + 3 + 2 × 2 × √3
    = (2 + √3
    ∴ √n = 2 + √3

    1
    =
    1
    = 2
    n2 + √3

    =
    1
    ×
    2 - √3
    = 2 - √3
    2 + √32 - √3

    ∴ √n +
    1
    = 2 + √3 + 2 - √3 = 4
    n

    Correct Option: B

    n = 7 + 4√3 = 7 + 2 × 2 × √3
    = 4 + 3 + 2 × 2 × √3
    = (2 + √3
    ∴ √n = 2 + √3

    1
    =
    1
    = 2
    n2 + √3

    =
    1
    ×
    2 - √3
    = 2 - √3
    2 + √32 - √3

    ∴ √n +
    1
    = 2 + √3 + 2 - √3 = 4
    n



  1. If   a + b + c = 0, then the value of
    a2 + b2 + c2
      is
    a2 − bc









  1. View Hint View Answer Discuss in Forum

    a + b + c = 0
    ⇒  b + c = –a
    On squaring both sides,
    ⇒  (b + c)2 = a2
    ⇒  b2 + c2 + 2bc = a2
    ⇒  a2 + b2 + c2 + 2bc = 2a2
    ⇒  a2 + b2 + c2 = 2a2 − 2bc = 2(a2 − bc)

    ∴ 
    a2 + b2 + c2
    =
    2(a2 − bc)
    = 2
    a2 − bca2 − bc

    Correct Option: C

    a + b + c = 0
    ⇒  b + c = –a
    On squaring both sides,
    ⇒  (b + c)2 = a2
    ⇒  b2 + c2 + 2bc = a2
    ⇒  a2 + b2 + c2 + 2bc = 2a2
    ⇒  a2 + b2 + c2 = 2a2 − 2bc = 2(a2 − bc)

    ∴ 
    a2 + b2 + c2
    =
    2(a2 − bc)
    = 2
    a2 − bca2 − bc