🧮 algebra

1. সমস্যাটি হলো: একটি সমান্তর ধারায় ১২ তম পদ $a_{12} = 77$ এবং প্রথম ২৩ পদের সমষ্টি $S_{23}$ নির্ণয় করতে হবে। 2. সমান্তর ধারার সাধারণ সূত্র হলো: $a_n = a + (n-1)d$, যেখানে $a$ প্র

1. Diketahui fungsi eksponen awal adalah $$f(x) = 2^{x^2} + 2$$. 2. Fungsi tersebut didilatasi dengan pusat (0,0) dan faktor skala 3. Dilatasi dengan pusat (0,0) dan faktor skala $

1. **State the problem:** Simplify or factor the expression $16x^4 + 4x^2y^2 + y^4$. 2. **Recognize the form:** This expression resembles a perfect square trinomial of the form $a^

1. Muammo: Asliddinda jami 48 ta $2 va $10 lik kupyuralar bor. Ularning jami puli 272 ga teng. $10 lik kupyuralar sonini toping. 2. Formulalar va qoidalar:

1. The problem asks to express the equation $0.5 = 2^{-1}$ in logarithmic form. 2. Recall the definition of logarithm: If $a^x = b$, then $\log_a b = x$.

1. **State the problem:** We need to find the value of $c$ in the equation of a circle given by $$x^2 + y^2 + ax + by + c = 0,$$

1. Let's start by understanding what an algebraic expression is. An algebraic expression is a combination of numbers, variables (like $x$ or $y$), and operations (such as addition,

1. Let's start by understanding the problem: we need to find the product of numbers expressed in their exponential forms. 2. The key formula for multiplying exponential expressions

1. **Problem statement:** Find the value of $\alpha - \beta$ where $\alpha$ and $\beta$ are roots of the quadratic equation $$3x^2 - 10x - 8 = 0$$ with $\alpha > \beta$. 2. **Formu

1. The problem states: Solve the logarithmic equation $\log_5 a = b$ for $a$. 2. Recall the definition of logarithms: $\log_b x = y$ means $b^y = x$.

1. **Problem Statement:** Given the quadratic equation $$2y^2 - 5y - 3 = 0$$ with roots $$\alpha$$ and $$\beta$$, find the value of $$\alpha + \beta$$. 2. **Formula Used:** For a q

1. **State the problem:** Solve the equation $A + b^2 = A + b$ for $b$. 2. **Simplify the equation:** Subtract $A$ from both sides to isolate terms involving $b$:

1. The problem is to perform factorization, which means expressing a mathematical expression as a product of its factors. 2. A common formula used in factorization is the differenc

1. **State the problem:** Simplify and expand the expression $$(4x-3)^2 - 1$$. 2. **Recall the formula:** The square of a binomial is given by $$(a-b)^2 = a^2 - 2ab + b^2$$.

1. **State the problem:** We need to make $d$ the subject of the formula given by $$P = \frac{1}{2} mn^2 - qd^2.$$ 2. **Rewrite the formula:** Start by isolating the term with $d^2

1. **State the problem:** Simplify the algebraic expression $$\alpha \beta^{2} + \alpha^{2} \beta$$. 2. **Identify common factors:** Both terms contain the variables $\alpha$ and $

1. **Énoncé du problème :** Résoudre dans $\mathbb{R}$ l'équation $A(x) = 0$ où $A(x) = -4x^4 + 20x^2 - 16$.

1. **Stating the problem:** Given the quadratic equation $$by^2 + xy + pd = 0,$$ where $$\alpha$$ and $$\beta$$ are its roots, show that $$\alpha + \beta = -\frac{r}{k}$$ and $$\al

1. **Problem 1:** Solve the equation $\left(x - \frac{1}{4}\right)^2 = -\frac{39}{16}$. 2. **Step 1:** Recognize that the right side is negative, so solutions will be complex numbe

1. We are asked to solve the quadratic equation $$2x^2 - x + 5 = 0$$ using the method of completing the square. 2. The general form of a quadratic equation is $$ax^2 + bx + c = 0$$

1. Énoncé du problème : Résoudre l'équation $$|2x - 3| + |x + 1| = 5$$ et montrer que $x=1$ est une solution. 2. Rappel des propriétés des valeurs absolues :