equations

It is given that x and y are integers in the following equation: $(x + y - 7)^2 + (y + 3x - 13)^2 = 0$ The value of $(x^3 + y^3)$ is ________ (in integer).

For positive integers p and q, with $\frac{p}{q} \neq 1$, $(\frac{p}{q})^{\frac{p}{q}} = p^{(\frac{p}{q}-1)}$. Then,

Consider the following equations of straight lines: Line L1: 2x - 3y = 5 Line L2: 3x + 2y = 8 Line L3: 4x - 6y = 5 Line L4: 6x - 9y = 6 Which one among the following is the correct...

$a + a + a + \dots + a = a^2b$ (n times) and $b + b + b + \dots + b = ab^2$ (m times), where a, b, n and m are natural numbers. What is the value of $(m + m + m + \dots + m)$ (n ti...

The temperature T in a room varies as a function of the outside temperature T₀ and the number of persons in the room p, according to the relation T = K (Θp + T₀), where Θ and K are...