if x+y = 12 and xy =32 find the value
of x^2+ y^2
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12
Answer:
80
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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.
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