Math Problem Statement
Solution
This image appears to be a math exam paper written in Vietnamese. It consists of four problems. Here's a quick overview of the content:
Problem 1 (4 points):
- Calculate the value of the expression:
- Calculate the value of the expression: at
Problem 2 (4 points):
- Expand the expression:
- Find such that is a perfect square.
Problem 3 (5 points):
- Show that for three real numbers , , and such that , the following holds:
- Show that is divisible by 6 when .
- Find all integer pairs that satisfy:
Problem 4 (6 points):
- In the square , the sides , , , and are extended to points , , , and such that . Prove that .
- Calculate the area of triangle .
- Prove the following geometric relations in triangle (with ):
- is the incenter of triangle .
- A line passing through and perpendicular to intersects at points and .
Would you like assistance with any specific problem or a detailed solution for any of the above? Let me know if you'd like to break down one of the tasks!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Geometric Proofs
Polynomials
Systems of Equations
Formulas
A = (63^2 - 47^2) / (215^2 - 105^2)
B = x^6 - 50x^5 + 50x^4 - 50x^3 + 50x^2 - 50x + 50
x^3 - 2x^2 + x - xy^2
a / (ab+1) + b / (bc+1) + c / (ca+1) = 1
x^2 - xy - 2022x + 2023y - 2024 = 0
Theorems
Properties of Polynomials
Perfect Square Theorem
Geometric Relations in Triangles and Squares
Suitable Grade Level
Grades 8-10
Related Recommendation
Step-by-Step Algebra and Geometry Solutions: Quadratics and Areas
Solutions to Algebra, Geometry, and Arithmetic Sequence Problems
Mathematics Assistance: Solve Algebra, Geometry, Calculus Problems Step-by-Step
Thay tỉ số và Giải các câu hỏi Đại số và Hình học
Solve Math Problems: Quadratic Equations, Derivatives, and Prime Numbers