Question

rezolvati ecuatia x+ 1/2 = 8/x+1. , x ≠ -1​

Answer 1

x + 1 / 2 = 8 / x + 1

x [ 2 ( x + 1 ) ] + x + 1 = 2 × 8

x ( 2x + 2 ) + x + 1 = 16

2x² + 2x + x + 1 = 16

2x² + 3x + 1 - 16 = 0

2x² + 3x - 15 = 0

Δ = b² - 4ac = 9 + 120 = 129

x₁.₂ = ( -b ± √Δ ) / 2a

x₁ = ( -3 + √129 ) / 4

x₂ = ( -3 - √129 ) / 4

S = { ( -3 + √129 ) / 4 , ( -3 - √129 ) / 4 }

Answer 2

Răspuns:

(x+1)/2=8/(x+1) , x≠-1

(x+1)(x+1)=16

(x+1)²=16

x+1=+-4

x+1=-4 => x=-4-1=-5

x+1=4 => x=4-1=3

x1=-5

x2=3

S={-5,3}