🧮 algebra

1. **Énoncé du problème :** Écrire sous la forme $a + b\sqrt{c}$ avec $a,b,c$ entiers les expressions suivantes :

1. **Problem:** Solve the equation $$\frac{x^2 - 9}{x + 3} = x^2 - 15$$. 2. **Formula and rules:** When dealing with rational expressions, first check for values that make the deno

1. **Stating the problem:** Simplify the expression $$\frac{\sqrt{18} \times \sqrt{6}}{\sqrt{15} \times \sqrt{5}}$$. 2. **Formula and rules:** Recall that $$\sqrt{a} \times \sqrt{b

1. مسئله: با استفاده از اتحادها حاصل عبارت (2x+3)^3 را بدست آورید. 2. فرمول مورد استفاده: برای مکعب مجموع داریم:

1. The problem asks to find the inverse relation $r^{-1}$ of the relation $r = \{ (x,y) \in \mathbb{R} \times \mathbb{R} \mid y = x^2 \}$. 2. The relation $r$ consists of all pairs

1. Vamos começar declarando o problema: isolar a incógnita $x$ na equação $$1 - \left(\frac{3}{4}\right)^x \cdot \frac{1}{\sqrt{3}} = \left(\frac{3}{4}\right)^x \sqrt{3} - \frac{1}

1. **State the problem:** Simplify the expression $4x^{3} - 4x^{2} + 4x$. 2. **Identify the common factor:** Each term has a factor of $4x$.

1. **State the problem:** Solve the quadratic equation $$6x^2 - 17x - 38 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$,

1. The problem is to simplify and evaluate the expression: $$\frac{314 \times (1.96)^2 \times 0.613 \times (1-0.613)}{(0.1)^2 \times (314-1) + 314 \times (1.96)^2 \times 0.613 \tim

1. **State the problem:** Solve the equation $2x - \frac{2}{x^2} = 0$ for $x$. 2. **Rewrite the equation:** Move terms to isolate fractions:

1. The problem asks whether the infinite series $$\sum_{k=1}^\infty \frac{5}{3^{k-1}}$$ is convergent or divergent. 2. This is a geometric series with the first term $$a = \frac{5}

1. **Stating the problem:** Solve the equation $$4^{x-3}\left(x-\frac{1}{2}\right) = 3^{x+\frac{1}{2}} - 2^{2x}$$ for $x$. 2. **Understanding the equation:** This is a transcendent

1. **Problem a:** Solve $\ln(x^2 - 1) = 1$ in $\mathbb{R}$. 2. The natural logarithm function $\ln(y)$ is defined for $y > 0$. So, first ensure the argument $x^2 - 1 > 0$ which mea

1. **State the problem:** Solve the simultaneous equations: $$x^2 + y^2 = 13$$

1. Diberikan sistem persamaan: $$ax + by - 3z = -3$$

1. **State the problem:** Simplify the expression $4(3+2x) - 2(3x-6) + 15x$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. The problem is to solve for $x$ in the equation $Q2$. 2. Since the problem statement is unclear or incomplete, we need a clear equation or expression to proceed.

1. **State the problem:** Solve the inequality $$\frac{2 - x}{x + 3} \geq 4$$ and give the solutions correct to 3 significant figures. 2. **Rewrite the inequality:** Move all terms

1. **Problem:** Solve for $x$ in the equation $\log x + \log(x - 1) = 1$. 2. **Formula and rules:** Use the logarithm property $\log a + \log b = \log(ab)$.

1. The problem asks about the meaning of the "ab" part with a bar over it. 2. In algebra, a bar over variables like \(\overline{ab}\) usually denotes the complex conjugate or the c

1. Мәселені түсіндіру: Геометриялық прогрессия құрайтын үш санның қосындысы 39-ға тең, ал олардың 3 негізіндегі логарифмдерінің қосындысы 6-ға тең. Прогрессияның еселігін табу кере