🧮 algebra

1. **Énoncé du problème :** Résoudre dans $\mathbb{R}$ l'équation quadratique $$x^2 - 5x + 6 = 0.$$ 2. **Formule utilisée :** Pour résoudre une équation quadratique $ax^2 + bx + c

1. **State the problem:** Simplify and expand the expression $\left(2\sqrt{x} + \frac{1}{\sqrt{x}}\right) x^5$ using algebraic manipulation and the binomial theorem if applicable.

1. The problem asks to express the quadratic expression $x^2 + 6x + 5$ in the form $(x + a)^2 + b$, where $a$ and $b$ are constants. 2. We use the method of completing the square.

1. The problem is to solve an exponential equation, which generally has the form $a^x = b$ where $a$ and $b$ are constants and $x$ is the variable. 2. The key formula to solve such

1. **State the problem:** Solve the equation $$52x - 120(5x) - 625 = 0$$ and understand how to factor the numbers easily. 2. **Rewrite the equation:** First, simplify the term $$-1

1. The problem is to simplify the expression: $$2(a + 2b) + 2b$$. 2. Use the distributive property: $$2(a + 2b) = 2 \times a + 2 \times 2b = 2a + 4b$$.

1. The problem is to provide an example of a function with its domain and codomain. 2. A function is a relation where each input (from the domain) is assigned exactly one output (i

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{63+x} = 0.15.$$\n\n2. **Formula and rules:** This is a rational equation where $x$ is in the numerator and $63+x$

1. **State the problem:** Solve the equation $$\frac{1}{x^2} - 16 = 0$$ for $x$. 2. **Rewrite the equation:** Add 16 to both sides to isolate the fraction:

1. **State the problem:** Solve the equation $$\frac{2h^2 - 1}{h^2 + 1} = 0$$ for the variable $h$. 2. **Recall the rule for fractions:** A fraction equals zero if and only if its

1. Let's start by stating a common algebra problem: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula or rule we use here is to isolate $x$ by performing inverse operat

1. Solve the equation $\frac{x}{3} + \frac{y}{4} = \frac{x}{2}$ for $y$. Step 1: Multiply both sides by 12 (the least common multiple of 3, 4, and 2) to clear denominators:

1. The problem asks us to find the largest whole number that is a factor of both 156 and 168. 2. This is the Greatest Common Divisor (GCD) or Greatest Common Factor (GCF) problem.

1. Stating the problem: Simplify the expression $$\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}$$. 2. Recall the rules:

1. **State the problem:** Simplify the expression $b \times \frac{400 - b}{2}$. 2. **Write the expression:** The expression is $b \times \frac{400 - b}{2}$.

1. Let's start with the first problem: Simplify $$\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}$$. 2. First, simplify the radicals inside the expression:

1. **State the problem:** Simplify the expression $$\frac{(5\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}$$. 2. **Rewrite radicals in simplest form:**

1. **State the problem:** We need to find the value of the function $g(x) = -4x + 7$ when $x = -1$. 2. **Formula used:** The function is given by $g(x) = -4x + 7$.

1. **Stating the problem:** Vi skal finne arealet av to rektangler med høyde 6 og bredder $x+4$ og $x+10$.

1. The problem is to solve everything, but since no specific problem is given, I will interpret this as solving a general algebraic equation example. 2. Let's solve the quadratic e

1. The problem is to define a bijective function. 2. A function $f: A \to B$ is called \textbf{bijective} if it is both \textbf{injective} (one-to-one) and \textbf{surjective} (ont