The sum of two positive numbers is 35 and their product is 286. The positive difference between them is:
9
Let the two numbers be \(a\) and \(b\), with \(a + b = 35\) and \(ab = 286\).
Use the identity \((a - b)^2 = (a + b)^2 - 4ab\).
Substitute the values: \((a - b)^2 = 35^2 - 4 \times 286 = 1225 - 1144 = 81\).
Take the positive square root: \(a - b = \sqrt{81} = 9\).
Hence, the positive difference between the numbers is 9.
Similar Questions
- The roots of the equation $3x^{2} + 5x - a = 0$ are the reciprocals of each other. What is the value of $a$?
- If the roots of the equation $(4 + m)x^2 + (m + 1)x + 1 = 0$ are equal, then find the values of m.
- The roots of the equation $y^2 - \sqrt{5} y - y + \sqrt{5} = 0$ are:
- The equation whose roots are $-2$ and $3$ is:
- If one of the roots of the equation $x^2 - 19x + 88 = 0$ is 8, then what is the other root?
- The sum of the roots of the equation $x^2 - 11x + 30 = 0$ is:
The positive value of m for which the roots of the equation ${12}{x}^2 + mx + 6 = 0$ are in the ratio of 2 : 3 is ______.
- Find the least positive integer such that its square is greater than 5 times of the integer by $-6$.
- If the roots of the equation $2x^2 - 3x + a = 0$ are in the ratio $1 : 2$, then find the value of $a$.
- Which of the quadratic equations below will not have real roots?
Important Questions from Quadratic Equation
If 2x 2+ 5x + 1 = 0, then one of the values of \(x - \frac{1}{{2x}}\) is:
If \(a-\frac{12}{a}=1\) , where a > 0, then the value of \(a^2+\frac{16}{a^2}\) is:
If x 2 – 3x + 1 = 0, then the value of \(\frac{(x^4+\frac{1}{x^2})}{(x^2+5x+1)}\) is:
If \(\sqrt{x}{}-{1\over\sqrt{x}}=\sqrt5\) , \(x \ne 0\) , then what is the value of \((x^4+{1\over{x^2}})\over(x^2+1) \) ?
If x 2 + \(\frac{1}{x^2}\) = 18, x > 0, then find the value of x 3 + \(\frac{1}{x^3}\) .
