最新の問題
(1) $x^3 = 1$ の虚数解の一つを $\omega$ とするとき、$\omega^3 = 1$ かつ $\omega^2 + \omega + 1 = 0$ を示す。 (2) 整式 $x^{...
複素数因数分解剰余の定理多項式
2025/3/27
The problem asks us to prove something about triangle $ABC$ given the equation $\vec{TA} + \vec{TB} ...
VectorsTrianglesCentroidGeometric Proofs
2025/3/27
The angle bisectors of triangle $ABC$ intersect the circumcircle of triangle $ABC$ at points $X, Y, ...
Triangle GeometryAngle BisectorsCircumcircleInscribed Angles
2025/3/27
The problem defines a function $F(x) = 2\sqrt{9-x^2}$ with domain $-3 \le x \le 3$. We need to find ...
FunctionsInverse FunctionsSquare RootsDomain and Range
2025/3/27
The image contains a set of mathematical problems related to a function $f(x)$. The tasks include ca...
CalculusDerivativesFunction AnalysisAsymptotesInverse FunctionsTangentsGraphingIntegrationArea Calculation
2025/3/27
(1) 整式 $P(x)$ を $x-a$ で割ったときの余りが $P(a)$ であることを証明する。（剰余の定理） (2) 整式 $P(x)$ を $x-1$ で割ると余りが 2 であり、$x+2$...
整式剰余の定理因数定理多項式の割り算
2025/3/27
The problem asks to calculate the area of a regular polygon circumscribed about a circle, given that...
PolygonsAreaPerimeterCircumscribedLimits
2025/3/27
The problem states "Доказать особину средње линије троугла" which translates to "Prove the property ...
TriangleMidlineParallel LinesSimilaritySAS Similarity
2025/3/27
Point $M$ is the midpoint of side $BC$ of triangle $ABC$. Prove that $\vec{AB} + \vec{AC} = 2\vec{AM...
VectorsTriangleMidpointVector AdditionGeometric Proof
2025/3/27
The problem consists of several sub-problems related to complex numbers. 1. Calculate $(2-4i)^2$ an...
Complex NumbersQuadratic EquationsGeometryTrigonometry
2025/3/27