🧮 algebra

1. The question is whether $x$ can be 0 in the context of the problem you are considering. 2. To determine if $x=0$ is valid, we need to check the conditions or domain restrictions

1. **State the problem:** Solve the equation $$(x - 2)^2 = (x + 7)^2 - 3x$$ 2. **Recall the formula:** The square of a binomial is $$(a \pm b)^2 = a^2 \pm 2ab + b^2$$

1. **State the problem:** Solve the quadratic equation $2x^2 - 8x + 8 = 4x - 8$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **Stating the problem:** Solve the first equation given: $$(X - 2)^2 = (X + 7)^2 - 3X$$

1. The problem asks to find the solution for the variable $w$ in the equation given, but the equation itself is missing from the message. 2. To solve for $w$, we need the explicit

1. **State the problem:** Solve the equation $3 \cdot 5^{0.2w} = 720$ for $w$. 2. **Isolate the exponential term:** Divide both sides by 3 to get

1. Let's start by understanding what "Case 3" means in the context of solving quadratic equations using the quadratic formula. 2. The quadratic formula is given by:

1. **State the problem:** We need to multiply the fraction $\frac{3}{5}$ by the mixed number $1 \frac{4}{7}$ and simplify the result. 2. **Convert the mixed number to an improper f

1. **State the problem:** Find the value of $\log \frac{1}{4}$. 2. **Recall the logarithm rule:** $\log \frac{a}{b} = \log a - \log b$.

1. The problem is to simplify the expression $\frac{1}{4} \log \frac{1}{4}$. 2. Recall the logarithm power rule: $a \log b = \log b^a$. We can rewrite the expression as $\log \left

1. The problem is to understand why when $u_n=1$, we assume $u_{n-1}$ and $u_{n-2}$ are also 1. 2. This situation often arises in sequences defined by recurrence relations, where e

1. **Énoncé du problème :** Résoudre l'équation $\frac{3}{2} = ... \times \frac{5}{2} \times ...$.

1. **Problem statement:** Show that the sequences $\{u_n\}$ satisfy the recurrence relation $$u_n = -3u_{n-1} + 4u_{n-2}$$ for each given sequence. 2. **Recurrence relation formula

1. **Problem statement:** Show that the sequence $\{u_n\}$ satisfies the recurrence relation $$u_n = -3u_{n-1} + 4u_{n-2}.$$\n\n2. **Understanding the recurrence relation:** This m

1. **Problem Statement:** Show that the sequence $\{u_n\}$ satisfies the recurrence relation $$u_n = -3u_{n-1} + 4u_{n-2}.$$\n\n2. **Understanding the recurrence relation:** This m

1. **State the problem:** Solve the first equation for $T_s$: $$2.5756 \times 10^{-8} T_s^4 + 3.68 T_s = 1343.74$$

1. Diketahui barisan aritmetika: 2, 5, 8, 11, ..., 74. Kita diminta mencari banyak suku barisan tersebut. 2. Rumus suku ke-n barisan aritmetika adalah:

1. **Problem statement:** Find at least three different sequences starting with the terms 1, 2, 4, each generated by a simple formula. 2. **Approach:** We want formulas that genera

1a. Rationalize the following expressions: 1. $$\frac{2}{3-\sqrt{2}} + \frac{1}{3+\sqrt{2}}$$

1. Problem: List the first 10 terms of each sequence and identify if any are arithmetic or geometric progressions. 2. a) Sequence starting at 10, subtracting 3 each time:

1. **Stating the problem:** We need to simplify the expression given as $8 \sqrt{584}$.