Daily Math · 2026-06-10

Question 1

Determine $a \in \mathbb{R}$ so that $A(1, 2)$, $B(3, 4)$, and $C(a, 5)$ are collinear.

Accepted Answer

$\overrightarrow{AB} = (2, 2)$, $\overrightarrow{AC} = (a - 1, 3)$. Collinear ⇒ $\dfrac{a - 1}{2} = \dfrac{3}{2} \Rightarrow a - 1 = 3 \Rightarrow a = 4$.

Answer

$2$

Answer

$3$

Answer

$4$

Answer

$5$

Question 2

The area of an equilateral triangle with side $a = 6$ equals:

Accepted Answer

$A = \dfrac{36\sqrt{3}}{4} = 9\sqrt{3}$.

Answer

$9$

Answer

$6\sqrt{3}$

Answer

$9\sqrt{3}$

Answer

$18$

Question 3

The solution of $\log_2(2x^2 + x + 1) - \log_2(x^2 - x + 2) = 1$ is:

Accepted Answer

$2x^2 + x + 1 = 2(x^2 - x + 2) \Rightarrow 2x^2 + x + 1 = 2x^2 - 2x + 4 \Rightarrow 3x = 3 \Rightarrow x = 1$.

Verify the domain: at $x = 1$, $2x^2 + x + 1 = 4 > 0$ and $x^2 - x + 2 = 2 > 0$, so both logs are defined. The solution set is $\{1\}$.

Answer

$\{1\}$

Answer

$\{-1\}$

Answer

$\{1, -3\}$

Answer

No real solution

Problems & worked solutions

Problem 1 — Lines in the Plane

Problem 2 — Solving Triangles

Problem 3 — Powers, Radicals, Logarithms