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If x + y = 12 …

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If x + y = 12 and xy = 32, Find the value of x² + y²

    • Posted by Ashish Singh 4 years, 4 months ago

    CBSE > Class 09 > Mathematics
    • 3 answers

    Kanav Dumra 4 years, 4 months ago

    X +y =12 and xy =32 The numbers which when multiplied gives 32 are 2 X 16 , 4 X 8. And in these numbers:- 8+4=12 So, X and Y are 8,4

    0Thank You

    R Maruthamani 4 years, 4 months ago

    =X+Y=12 =XY =32 AS, 8+4=12 8×4=32 Therefore, X^2+Y^2=8^2+4^2 So,8^2+4^2=64+16 =80

    0Thank You

    Yogita Ingle 4 years, 4 months ago

      x+y=12 ------Equation 1

    Squaring equation 1 on both sides 

      (x+y)² = 12²-----Equation 2

    (a+b)²=a²+2ab+b²

    Now comparing (x+y)² with (a+b)² here a=x and b=y 

    So Equation 2 becomes 

      (x+y)² = 12²

      x²+2xy+y² =12²

      x²+y² = 144 - 2xy----Equation 3

    But in question its given that xy= 32 

    So, substituting xy = 32 in equation 3

       x²+y² =144-2*32

      x²+y² =144-64 = 80.

    0Thank You

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