Solve the following equation by factorization:
4x² - 4ax + (a² - b²) = 0, where a, b ∈ R.

Question

Solve the following equation by factorization: 4x^2 - 4ax + (a^2 -b^2) = 0, where a, b ∈ R.

KnowledgeBoat · Accepted Answer

Given, ⇒ 4x2 - 4ax + (a2 - b2) = 0 ⇒ (4x2 - 4ax + a2) - b2 = 0 ⇒ [(2x)2 - 2 × a × 2x + (a)2] - b2 = 0 ⇒ (2x - a)2 - b2 = 0 ⇒ (2x - a + b)(2x - a - b) = 0 ⇒ (2x - a + b) = 0 or (2x - a - b) = 0 [Using Zero-product rule] ⇒ 2x = a - b or 2x = a + b ⇒ x = or x = . Hence, x = .

Mathematics

Solve the following equation by factorization:
4x² - 4ax + (a² - b²) = 0, where a, b ∈ R.

Quadratic Equations

Related Questions

Solve the following equation by factorization:
3a²x² + 8abx + 4b² = 0, a ≠ 0

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5x² - 12x - 9 = 0, when (i) x ∈ I (ii) x ∈ Q

Solve the following equation by factorization:
2x² - 11x + 15 = 0, when (i) x ∈ N (ii) x ∈ I

Mathematics

Solve the following equation by factorization:4x2 - 4ax + (a2 - b2) = 0, where a, b ∈ R.

Quadratic Equations

Related Questions

Solve the following equation by factorization:3a2x2 + 8abx + 4b2 = 0, a ≠ 0

Solve the following equation by factorization:5x2 - 12x - 9 = 0, when (i) x ∈ I (ii) x ∈ Q

Solve the following equation by factorization:2x2 - 11x + 15 = 0, when (i) x ∈ N (ii) x ∈ I

Solve the following equation by factorization:
4x² - 4ax + (a² - b²) = 0, where a, b ∈ R.

Solve the following equation by factorization:
3a²x² + 8abx + 4b² = 0, a ≠ 0

Solve the following equation by factorization:
5x² - 12x - 9 = 0, when (i) x ∈ I (ii) x ∈ Q

Solve the following equation by factorization:
2x² - 11x + 15 = 0, when (i) x ∈ N (ii) x ∈ I