Question

What is the square root of 4x⁴ + 8x³ - 4x + 1?
1. 2x² - 2x - 1
2. 2x2​ - x - 1
3. 2x2​ + 2x + 1
4. 2x2​ + 2x - 1

Answer 1

Correct Answer - Option 4 : 2x2​ + 2x - 1

Given:

The given expression is 4x⁴ + 8x³ - 4x + 1

Formula used:

(a + b - c)² = a² + b² + c² + 2ab - 2bc - 2ca

Calculation:

4x4 + 8x3 - 4x + 1

⇒ 4x4 + 8x3 - 4x + 1 + 4x² - 4x²

⇒ 4x4 + 4x2 + 1 + 8x3 - 4x - 4x2

⇒ (2x²)² + (2x)² + (1)² + 2 × 2x2 × 2x - 2 × 2x × 1 - 2 × 2x2 × 1

⇒ (2x² + 2x - 1)²

So, \(\sqrt{4x^4 + 8x^3 - 4x + 1}\)

⇒ \(\sqrt{(2x^2 + 2x - 1)^2}\)

⇒ 2x2 + 2x - 1

∴ The square root of 4x4 + 8x3 - 4x + 1 is 2x2 + 2x - 1.