🧮 algebra

1. The problem states that \(\alpha\) and \(\beta\) are the roots of a quadratic equation. We need to find relationships involving these roots. 2. For a quadratic equation of the f

1. **Problem Statement:** Solve the linear equation involving fractions, for example, $$\frac{2x}{3} + \frac{1}{4} = \frac{5x}{6} - \frac{1}{2}$$. 2. **Formula and Rules:** To solv

1. **State the problem:** Solve the quadratic equation $2x^2 - x + 5 = 0$. 2. **Formula used:** The quadratic formula for $ax^2 + bx + c = 0$ is

1. The problem is incomplete as given: "Let a->" does not specify what is asked or what expression is involved. 2. To assist you properly, please provide the full problem statement

1. The problem is incomplete as given: \left[\; is an opening bracket without a closing part or expression inside. 2. To solve or simplify expressions involving brackets, we need t

1. Nyatakan masalah: Fungsi kuadratik diberikan oleh $$f(x) = p(x + q)^2 + r$$ dengan pemalar $p$, $q$, dan $r$. Fungsi ini mempunyai nilai minimum $-4$ dan paksi simetri $x = 3$.

1. **State the problem:** Given $a+b=10$ and $ab=21$, find $(a-b)^2$. 2. **Recall the formula:** We know that $(a-b)^2 = (a+b)^2 - 4ab$.

1. **Nyatakan masalah:** Diberi fungsi kuadratik $$f(x) = 3(x + p)^2 + 2$$ dengan titik minimum pada $$(1, q)$$. Kita perlu cari nilai $p$, nilai $q$, dan persamaan paksi simetri.

1. **State the problem:** We are given an arithmetic progression (A.P.) with the first few terms 72, 68, 64, 60, … and we need to find which term is zero. 2. **Recall the formula f

1. **State the problem:** We are given an arithmetic progression (A.P.) with the first few terms 72, 68, 64, 60, … and we need to find which term is zero. 2. **Recall the formula f

1. The problem is to solve the equation or expression given previously, but now using a different method. 2. Since the original problem is not restated, let's assume it involves so

1. **State the problem:** Find the 19th term of the arithmetic progression (AP) 54, 51, 48, ... 2. **Formula used:** The $n$th term of an AP is given by $$a_n = a_1 + (n-1)d$$ wher

1. The problem is to determine if the 19th term of a given sequence is 0. 2. To solve this, we need the explicit formula or rule for the sequence to find the 19th term.

1. **State the problem:** We have an arithmetic progression (A.P.) with first term $a_1 = 54$, common difference $d = 51 - 54 = -3$, and we want to find the number of terms $n$ suc

1. Masalah yang diberikan adalah menyelesaikan pertidaksamaan $$|2x - 1| \leq |x + 3|$$. 2. Kita gunakan definisi nilai mutlak dan sifat pertidaksamaan: $$|A| \leq |B| \iff -|B| \l

1. Diberikan pertidaksamaan $$\sqrt{x} + 1 > 3 - x$$. 2. Tujuan kita adalah mencari nilai $x$ yang memenuhi pertidaksamaan ini.

1. **Problem statement:** Given a binary operation $*$ on real numbers defined by $a * b = a + b + \frac{2ab}{5}$, evaluate (i) $3 * 2$, (ii) $2 * (4 * 5)$. 2. **Formula and rules:

1. **State the problem:** Solve the quadratic equation $x^2 + 18x - 360 = 0$. 2. **Formula used:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ wher

1. **Problem:** Find the value of $a$ such that the lines $L_1: 3x - ay - 2 = 0$ and $L_2: 6x - 4y + 3 = 0$ are parallel. 2. **Formula and rule:** Two lines $Ax + By + C = 0$ and $

1. **State the problem:** Simplify the expression $$(x-2y)(y-3x)+(x-y)(x-3y)-(y-3x)(4x-5y).$$ 2. **Use the distributive property (FOIL) to expand each product:**

1. **State the problem:** Simplify the expression $$(x-2y)(y-3x)+(x-y)(x-3y)-(y-3x)(4x-5y).$$ 2. **Recall the distributive property:** To simplify, we expand each product using $$(