Question

Calcule:
a) (x+1)² + (x+2)²
B) (3x-1)² + (x+1)²

Answer 1

a) (x + 1)² + (x + 2)²
(x² + 2 . x . 1 + 1²) + (x² + 2 . x . 2 + 2²)
x² + 2x + 1 + x² + 4x + 4
x² + x² + 2x + 4x + 1 + 4
2x² + 6x + 5 = 0
a = 2, b = 6, c = 5

Δ = b² - 4ac
Δ = 6² - 4 . 2 . 5
Δ = 36 - 40
Δ = -4

x = $\frac{-b \pm \sqrt{\Delta} }{2a}$
x = $\frac{-6 \pm \sqrt{-4} }{2 . 2}$
x = $\frac{-6 \pm \sqrt{-4} }{4}$

b) (3x - 1)² + (x + 1)²
(3x² - 2 . 3x . 1 + 1²) + (x² + 2 . x . 1 + 1²)
9x² - 6x + 1 + x² + 2x + 1
9x² + x² - 6x + 2x + 1 + 1
10x² - 4x + 2 = 0
a= 10, b = -4, c = 2

Δ = b² - 4ac
Δ = (-4)² - 4 . 10. 2
Δ = 16 - 80
Δ = -64

x = $\frac{-b \pm \sqrt{\Delta} }{2a}$
x = $\frac{- (-4) \pm \sqrt{-64} }{2 . 10}$
x = $\frac{4 \pm \sqrt{-64} }{20}$