Question

Solve : 2(x² + 1) (2x + 1) = (x² + 6x + 4)(x² - 4x -1)​

Answer 1

Answer:

• X1 = -3

• X2 = -1

• X3 = 3 - √11

• X4 = 3 + √11

Step-by-step explanation:

⟹ 2(x² + 1) (2x + 1) = (x² + 6x + 4)(x² - 4x -1)

⟹ (2x² + 2) × (2x + 1) = x⁴ - 4x³ - x² + 6x³ - 24x² - 6x + 4x² - 16x - 4

⟹ 4x³ + 2x³ + 4x + 2 = x⁴ + 2x³ - 21x² - 22x - 4

⟹ 4x³ + 2x² + 4x + 2 - x⁴ + 2x³ + 21x² + 22x + 4 = 0

⟹ 2x³ + 23x² + 26x + 6 - x⁴ = 0

⟹ - x⁴ + 2x³ + 23x² + 26x + 6 = 0

⟹ - x⁴ - x³ + 3x³ + 3x² + 20x² + 20x + 6x + 6 = 0

⟹ - x³ × (x+1) + 3x² × (x+1) + 20x × (x+1) + 6(x+1) = 0

⟹ - (x + 1) × (x³ - 3x² - 20x - 6) = 0

⟹ (x + 1) × (x + 3) × (x² - 6x - 2) = 0

⟹ x + 1 = 0 , x + 3 = 0 , x² - 6x - 2 = 0

Therefore,

• x = -1
• x = -3
• x = 3 - √11 or 3 + √11