🧮 algebra

1) Bài toán: Cho hai số dương $x, y$ thỏa mãn phương trình $$x(x^3 + y^3) + 6xy(x + y - 2) = (x + y)^2(xy + 4).$$

1. مسئله را بیان می‌کنیم: دنباله‌ای به صورت بازگشتی تعریف شده است: $$a_n = 2a_{n-1} - a_{n-2}$$

1. **Problemstellung:** Bestimme eine ganzrationale Funktion vierten Grades $f(x)$, die zur y-Achse symmetrisch ist, durch den Ursprung geht, bei $x=3$ eine Nullstelle hat mit Stei

1. **Problem statement:** Bestimmen Sie eine ganzrationale Funktion dritten Grades, deren Graph zum Koordinatenursprung symmetrisch ist. Der Graph hat eine Nullstelle bei $x=2$, di

1. **State the problem:** If 15 is subtracted from the product of 4 and a certain number, the result is 5. Find the number. 2. **Set up the equation:** Let the certain number be $x

1. **State the problem:** We need to find a number such that when it is multiplied by 4 and then 7 is added to the product, the result is 19. 2. **Set up the equation:** Let the nu

1. **State the problem:** We are given the sum of the ages of Jerry, Sowane, and Sashi as 64. 2. **Given data:**

1. نبدأ بكتابة المسألة: تحليل العبارة الجبرية $$x^2 + 7x + 4$$. 2. نبحث عن عاملين للعدد 4 مجموعهما 7، لكن 4 عدد أولي ولا يوجد عاملان صحيحان يحققان ذلك.

1. The problem is to understand and simplify the expression $15x^2y$. 2. This expression is a product of a constant coefficient 15 and variables $x^2$ and $y$.

1. **State the problem:** We need to find how many books are in a set if the total cost is 72 and each book costs 4.50. 2. **Formula used:** To find the number of books, use the fo

1. **State the problem:** You take 45 minutes to get dressed and have breakfast each morning. Breakfast takes 17 minutes. We need to find how long it takes to get dressed. 2. **For

1. **State the problem:** A packet of crayons and an exercise book together cost 2.70. A packet of crayons costs 1.25.

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $2x + 5 = 15$. 2. The formula to solve for $x$ is to isolate $x$ on one side of the equation. We do this

1. Berilgan ifoda: $$\frac{\left(\frac{1}{a} + \frac{1}{b} - \frac{c}{ab}\right)(a + b + c)}{\frac{1}{a^2} + \frac{1}{b^2} + \frac{2}{5}ab - \frac{c^2}{a^2b^2}}$$ 2. Qiymatlarni qo

1. The problem is to solve the equation without using the dollar sign symbol. 2. Since no specific equation is given, let's clarify that in math, the dollar sign is not used in equ

1. **State the problem:** We have the quadratic equation $$x^2 + kx + 15 - k = 0$$ and need to find the values of $$k$$ such that it has two distinct real roots. 2. **Formula and r

1. Diberikan persamaan $$\sqrt{1 + \log_3 x^5 + \sqrt{1 + \log_3 x^5 + \sqrt{1 + \log_3 x^5 + \cdots}}} = 3$$. Kita diminta mencari nilai dari $$\log_3 x^{81}$$. 2. Misalkan $$y =

1. **Problem 1.16:** Calculate $ (6\sqrt{5} + 2\sqrt{3}) \times 9\sqrt{5} $. 2. **Formula and rules:** Use distributive property: $ (a+b)c = ac + bc $. Also, $ \sqrt{a} \times \sqr

1. **Problem:** Simplify the expression $5\sqrt{7} \times (3\sqrt{2} + 7\sqrt{7})$. 2. **Formula and rules:**

1. **Planteamiento del problema:** Tenemos la función lineal $$f(x) = 5x + 6$$ y debemos resolver varias preguntas relacionadas con esta función. 2. **Fórmula general de funciones

1. The problem is to deduce a property or value graphically from the function $f$. 2. To solve this, we first need the explicit form of the function $f(x)$ or its graph.