The sum of two positive numbers is 44 and their product is 228. The positive difference between them is:
32
Let the numbers be x and y, with \(x+y=44\) and \(xy=228\).
Their difference satisfies \((x-y)^2=(x+y)^2-4xy=44^2-4\times228=1936-912=1024\).
\(x-y=\sqrt{1024}=32\).
Hence, the positive difference between the two numbers is 32.
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
