The sum of two positive numbers is 51 and their product is 230. The positive difference between them is:
41
Let the two numbers be x and y, with \(x + y = 51\) and \(xy = 230\).
Using the identity \((x-y)^2 = (x+y)^2 - 4xy\), we get \((x-y)^2 = 51^2 - 4 \times 230\).
This gives \((x-y)^2 = 2601 - 920 = 1681\).
So \(x - y = \sqrt{1681} = 41\).
Hence, the positive difference between the numbers is 41.
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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:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
