The sum of two positive numbers is 30 and their product is 176. The positive difference between them is:
14
Let the two numbers be \(a\) and \(b\) with \(a + b = 30\) and \(ab = 176\).
Use the identity \((a - b)^2 = (a + b)^2 - 4ab\).
Substitute the values: \((a - b)^2 = 30^2 - 4 \times 176 = 900 - 704 = 196\).
Take the positive square root: \(a - b = \sqrt{196} = 14\).
Hence, the positive difference between the two numbers is 14.
Similar Questions
- If $a = 9$, $b = -5$ and $c = -4$, then find the value of $a^{3} + b^{3} + c^{3}$.
- If $x^2 = y+z, y^2 = z+x$ and $z^2 = x+y$, then find the value of $\frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1}$.
- If $x^4 + \frac{1}{x^4} = 322$ and $x > 1$, then what is the value of $x^3 - \frac{1}{x^3}$?
- If $x - \frac{1}{x} = 5$, find the value of $x^4 + \frac{1}{x^4}$.
- Find the value of $a^2 + b^2 + c^2 - 2ab + 2ac - 2bc$, if $a = x + y, b = x - y$ and $c = 2x - 1$
- If $x + \frac{1}{x} = 2$, then the value of $x^{2} + \frac{1}{x^{2}} = ?$
- If $x + y + z = 0$, then what will be the value of $\frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy}$ ?
- If $x^3 + \frac{1}{x^3} = 18$, then what will be the value of $x + \frac{1}{x}$?
- If $x + \frac{1}{x} = 5$
Then the value of $\frac{3x}{2x^2 + 2 - 5x}$ will be: - If $3a + 4b = 2$ and $ab = \frac{1}{36}$, then $27a^3 + 64b^3$ is:
Important Questions from Algebra
If 2x – y = 2 and xy = \(\frac{3}{2}\) , then what is the value of x 3– \(\frac{{{y^3}}}{8}\) ?
If (10a 3+ 4b 3) : (11a 3- 15b 3) = 7 : 5, then (3a + 5b) : (9a - 2b) =?
- If 4sin 2 θ = 3(1+ cos θ), 0° < θ < 90°, then what is the value of (2tan θ + 4sin θ - sec θ)?
The value of:
\(\frac{{\sin 23^\circ \cos 67^\circ + \sec52^\circ \sin38^\circ + \cos 23^\circ \sin 67^\circ + \rm cosec52^\circ \cos 38^\circ }}{{\rm cose{c^2}20^\circ - {{\tan }^2}70^\circ }}\)
If (x + y) 3+ 27(x - y) 3= (Ax - 2y)(Bx 2+ Cxy + 13y 2), then the value of A - B - C is:
