4
Finding Integer Difference from Sum and Product
Let the two integers be denoted by $x$ and $y$.
- Given the sum: $x + y = 26$
- Given the product: $x \times y = 165$
- We need to find the difference: $|x - y|$.
We can use the algebraic identity relating the sum, product, and difference of two numbers:
$ (x - y)^2 = (x + y)^2 - 4xy $
Substitute the given values into the identity:
$ (x - y)^2 = (26)^2 - 4(165) $
Calculate the terms:
$ (26)^2 = 676 $
$ 4 \times 165 = 660 $
Now, compute $(x - y)^2$:
$ (x - y)^2 = 676 - 660 $
$ (x - y)^2 = 16 $
To find the difference, take the square root of both sides:
$ x - y = \sqrt{16} $
$ x - y = \pm 4 $
The difference between the two integers is $4$.
Important Questions from Algebra
- If $Pe^x = Qe^{-x}$ for all real values of $x$, which one of the following statements is true?
The relationship between two variables $x$ and $y$ is given by $x + py + q = 0$ and is shown in the figure. Find the values of $p$ and $q$.
Note: The figure shown is representative.
The real variables $x, y, z$ and the real constants $p, q, r $ satisfy
$\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$
Given the denominators are non-zero, the value of $px + qy + rz$ isThe complex function
$e^{-\left(\frac{2}{z-1}\right)}$
has __________________Consider two matrices: $P = \begin{bmatrix} 1 & 2 \\ 0 & 1 \end{bmatrix}$ and $Q = \begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}$.
Which of the following statement is/are true?
