Find the Value of a²+b² is

If 4x2+12xy-8x+9y2-12y = (ax+by)(ax+by-4). Then the value of a²+b² is:

  1. 13
  2. 25
  3. 5
  4. 10
Monis Rasool Professor Asked on 20th September 2015 in Maths.
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  • 1 Answer(s)

    Answer: (1) 13

    Explanation:-

    4x2 + 12xy – 8x + 9y2– 12y = (ax + by) (ax + by – 4)
    (2x)2 + 2 x 2X x 3y – 8x + (3y)2 – 12y = (ax + by) (ax + by – 4)
    (2x + 3y)2 – 4(2x + 3y) = (ax + by) (ax + by – 4)
    (2x + 3y) (2x + 3y – 4) = (ax + by) (ax + by – 4)
    Comparing on both side,
    Then, a = 2  & b = 3
    The value of a2 + b2 = 22 + 32
    = 2 x 2 + 3 x 3
    = 4 + 9
    = 13

    Hence, the answer is (1) 13.

     

    Anurag Mishra Professor Answered on 21st September 2015.
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