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Home Aptitude Elementary Algebra See What Others Are Saying!
  • 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


  • More questions

    • 1. Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

    • Options
    • A. 2 : 3
    • B. 1 : 1
    • C. 3 : 4
    • D. 4 : 3
    • Discuss
    • 2. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

    • Options
    • A. 65 sec
    • B. 89 sec
    • C. 100 sec
    • D. 150 sec
    • Discuss
    • 3. What was the day of the week on 17th June, 1998?

    • Options
    • A. Monday
    • B. Tuesday
    • C. Wednesday
    • D. Thursday
    • Discuss
    • 4. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:

    • Options
    • A. 279
    • B. 283
    • C. 308
    • D. 318
    • Discuss
    • 5. 
      1872/ ? ? = 234

    • Options
    • A. 324
    • B. 64
    • C. 8
    • D. 256
    • Discuss
    • 6. 
      For every 4 leaps taken by a dog, a cat takes 5 leaps in the same time. But distance covered in 3 leaps of dog is same as that of 4 leaps of cat. Then what is the ratio of speed of dog and cat?

    • Options
    • A. 15 : 14
    • B. 16 :15
    • C. 12 :11
    • D. 10 : 9
    • Discuss
    • 7. 
      A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?

    • Options
    • A. 34%
    • B. 46%
    • C. 54%
    • D. 66%
    • Discuss
    • 8. 
      1, 9, 25, 49, 81,?

    • Options
    • A. 90
    • B. 135
    • C. 121
    • D. 125
    • Discuss
    • 9. 
      An accurate clock shows the time as 3:00 after hour hand has moved 135°, the time would be?

    • Options
    • A. 7:30
    • B. 6:30
    • C. 8:00
    • D. 9:30
    • Discuss
    • 10. 
      P.V. Narsihma Rao was elected party leader on 29th may, 1991. What was the day of the week?

    • Options
    • A. Tuesday
    • B. Friday
    • C. Wednesday
    • D. Sunday
    • Discuss


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