Class 10 Mathematics Quadratic Equations Bengali

Class 10 Mathematics (দশম শ্রেণি গণিত) – একচল বিশিষ্ট দ্বিঘাত সমীকরণ

This product provides a detailed, step-by-step solution to a typical Class 10 Mathematics problem on quadratic equations in one variable, as per the Bengali medium syllabus. It is ideal for students preparing for Madhyamik or similar exams.

Problem Statement

Solve:
(x + 2)/(x - 2) + 6 * (x - 2)/(x + 2) = 5, where x ≠ 2, -2.

Solution Approach

• Substitution: Let a = (x + 2)/(x - 2). The equation simplifies to a + 6/a = 5.
• Simplify: Multiply both sides by a to get a² - 5a + 6 = 0.
• Factorize: Using middle term factorization: (a - 3)(a - 2) = 0, so a = 3 or a = 2.
• Back-substitute:
  Case 1: a = 3 ⇒ (x + 2)/(x - 2) = 3 ⇒ x = 4.
  Case 2: a = 2 ⇒ (x + 2)/(x - 2) = 2 ⇒ x = 6.

Answer: x = 4 or x = 6.

This solution is presented in a clear, logical manner, helping students understand the method of substitution and factorization for solving quadratic equations. Perfect for self-study and exam preparation.