The sum of two positive numbers is 67 and their product is 1012. The positive difference between them is:
21
Let the two numbers be \(x\) and \(y\), with \(x + y = 67\) and \(xy = 1012\).
Using the identity \((x-y)^2 = (x+y)^2 - 4xy\).
Substitute the values: \((x-y)^2 = 67^2 - 4 \times 1012 = 4489 - 4048 = 441\).
\(x - y = \sqrt{441} = 21\).
Hence, the positive difference between the two numbers is 21.
Similar Questions
Simplify: $3((\frac{5}{3})x^2 - 28x + 15) - 5(x^2 + 6x - 15)$
- The product of two positive numbers is 1445. If the first number is five times of the second number, then the sum of the two numbers is:
- The value of $x$ satisfying the equation $x^2 + a^2 = (b - x)^2$ is:
- Out of four consecutive numbers, the sum of the first two numbers is equal to the fourth number. What is half of the sum of the four numbers?
- If $p = 5 - 2\sqrt{6}$, then find the value of $p^2 + \frac{1}{p^2}$
- Which of the following number, when added to itself 14 times gives 135 as result?
- Simplify $x(7x - 2) + 5(x^2 - 3) + 13$.
- What is the number of all positive solutions of the equation $|x \times 1| = 0$ ?
- If $a + b = 5$ and $ab = 13$, then what will be the value of $a^3 + b^3$?
- The value of $p^2 - 7p + 12$ at $p = 3$ is:
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:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
