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  • Question
  • If a3 ? b3 = 56 and a ? b = 2, then the value of ( a2 + b2 ) is :


  • Options
  • A. ? 10
  • B. ? 12
  • C. 20
  • D. 18

  • Correct Answer
  • 20 

    Explanation

    As we know from the algebra formula,
    (a ? b)3 = a3 ? b 3 ? 3ab (a ? b) .......................(1)
    As per given question,
    a3 ? b 3 = 56 and a ? b = 2
    Put these value in above equation (1) . We will get,
    ? 23 = 56 ? 3ab x 2
    ? 8 = 56 ? 3ab x 2
    ? 8 = 56 ? 6ab
    ? 6ab = 56 ? 8 = 48
    ? ab = 8 ...................... (i)
    ? a2 + b2 = (a ? b)2 + 2ab
    ? a2 + b2 = (a ? b)2 + 2ab
    Put the value of
    ? a2 + b2 = 22 + 2 x 8
    ? a2 + b2 = 4 + 16 = 20


  • Elementary Algebra problems


    Search Results


    • 1. 
      If (5x2 ? 3y2) : xy = 11 : 2, then the positive value of
      x
      is :
      y

    • Options
    • A. 7 2
    • B. 5 2
    • C. 3 2
    • D. 5 3
    • Discuss
    • 2. 
      If P = (0.08) 2, Q = 1/(0.08) 2 and R = (1 ? 0.08) 2 ? 1, then out of the following the true relation is

    • Options
    • A. Q < P and P = R
    • B. P < Q and P = R
    • C. Q < R < P
    • D. R < P < Q
    • Discuss
    • 3. 
      The sum of two numbers is 24 and their product is 143. The sum of their squares is

    • Options
    • A. 296
    • B. 295
    • C. 290
    • D. 228
    • Discuss
    • 4. 
      The product of two alternate odd integers exceeds three times the smaller by 12. What is the larger integer?

    • Options
    • A. 9
    • B. 7
    • C. 3
    • D. 5
    • Discuss
    • 5. 
      What is the solution of the equations x - y = 0.9 and 11(x + y) -1 = 2?

    • Options
    • A. x = 3.2, y = 2.3
    • B. x = 1, y = 0.1
    • C. x = 2, y = 1.1
    • D. x = 1.2, y = 0.3
    • Discuss
    • 6. 
      If x = 2 + ?3, then the value of ?x +
      1
      is :
      ?x

    • Options
    • A. ?3
    • B. ?6
    • C. 2 ?6
    • D. 6
    • Discuss
    • 7. 
      If 5a +
      1
      = 5, the value of 9a2 +
      1
      is
      3a 25a2

    • Options
    • A. 34 5
    • B. 39 5
    • C. 42 5
    • D. 52 5
    • Discuss
    • 8. If a, b, c are real and a3 + b3 + c3 = 3abc and a + b + c ≠ 0 , then the relation between a, b, c will be

    • Options
    • A. a + b = c
    • B. a + c = b
    • C. a = b = c
    • D. b + c = a
    • Discuss
    • 9. 
      The line passing through the points (? 2, 8) and (5, 7)

    • Options
    • A. does not cut any axes
    • B. cuts x- axis only
    • C. cuts y - axis only
    • D. cuts both the axes
    • Discuss
    • 10. 
      If the difference of two numbers is 3 and the difference of their squares is 39; then the larger number is:

    • Options
    • A. 9
    • B. 12
    • C. 13
    • D. 8
    • Discuss


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