The sum of two positive numbers is 14 and their product is 45. The positive difference between them is:
4
Let the numbers be a and b, with \(a+b=14\) and \(ab=45\).
Using \((a-b)^2 = (a+b)^2-4ab = 196-180 = 16\).
\(a-b = \sqrt{16} = 4\).
Hence, the positive difference between the two numbers is 4.
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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 + \(\frac{1}{x^3}\) .
