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  • Question

  • If a + b + c = 8, then the value of (a ? 4)3 + (b ? 3)3 + (c ? 1)3 ? 3 (a ? 4) (b ? 3) (c ? 1) is


  • Options
  • A. 2
  • B. 4
  • C. 1
  • D. 0

  • Correct Answer
  • 0 

    Explanation

    We have p3 + q3 + r3 ? 3pqr = (p + q + r) (p2 + q2 + r2 ?pq ? qr - rp)
    Here p = a ? 4, q = b ? 3, r = c ?1
    So, given expression is (p + q + r) (p2 + q2 + r2 ? pq ? qr ? rp)
    = (a ? 4 + b ? 3 + c ? 1) (p2 + q2 + r2 ? pq ? qr ? rp)
    = (a + b + c ? 8) (p2 + q2 + r2 ? pq ? qr ? rp)
    = (8 ? 8) (p2 + q2 + r2 ? pq ? qr ? rp)
    ? (a ? 4)3 + (b ? 3)3 + (c ? 1)3 ? 3 (a ? 4) (b ? 3) (c ? 1) = 0

    • Elementary Algebra problems

    Search Results

    • 1. 
      If x = ?a +
      1
      		, y = ?a -
      1
      		, then the value of
      ?a
      		 ?a
      x4 + y4 - 2x2 y2 is

    • Options
    • A. 16
    • B. 20
    • C. 10
    • D. 5
      • Discuss
    • 2. 
      The area (in sq. unit) of the triangle formed by the three graphs of the equations x = 4, y = 3, and 3x + 4y = 12, is

    • Options
    • A. 12
    • B. 10
    • C. 6
    • D. 8
      • Discuss
    • 3. 
      The area of the triangle formed by the lines 5x + 7y = 35, 4x + 3y = 12 and x-axis is

    • Options
    • A. 160 sq.unit 13
    • B. 150 sq.unit 13
    • C. 140 sq.unit 13
    • D. 10 sq.unit
      • Discuss
    • 4. 
      If x =
      4ab
      		, then the value of
      x + 2a
      		+
      x + 2b
      		is
      a + b x - 2a
      		 x - 2b

    • Options
    • A. a
    • B. b
    • C. 0
    • D. 2
      • Discuss
    • 5. 
      If 2x -
      1
      		= 6, then the value of x2 +
      1
      		is
      2x 16x2

    • Options
    • A. 19 2
    • B. 17 2
    • C. 18 2
    • D. 15 2
      • Discuss
    • 6. 
      Minimum value of x2 +
      1
      		- 3 is
      x2 + 1

    • Options
    • A. - 3
    • B. - 2
    • C. 0
    • D. - 1
      • Discuss
    • 7. 
      The shaded region represents

    • Options
    • A. y ? x
    • B. y ? ? x
    • C. y ? x
    • D. y ? ? x
      • Discuss
    • 8. 
      If x = a ? b, y = b ? c, z = c ? a, then the numerical value of the algebraic expression x3 + y + z ? 3xyz will be

    • Options
    • A. a + b + c
    • B. 0
    • C. 4 (a + b + c)
    • D. 3 abc
      • Discuss
    • 9. 
      What is the greatest number that divides 263, 935 and 1383 leaving a remainder of 7 in each case?

    • Options
    • A. 30
    • B. 31
    • C. 32
    • D. 35
      • Discuss
    • 10. 
      If (x+2) is the HCF of x 2 + ax + b and x 2 + cx + d , then which one of the following is correct?

    • Options
    • A. a + c = b + d
    • B. 2a + b = 2c + d
    • C. b + 2c = 2a + d
    • D. b - 2c = 2a - d
      • Discuss

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