Rownaniex3+3x2+2x+4 = (x+2)2.... Question from @Jarass

October 2018 2 8 Report

Rownanie

x3+3x2+2x+4 = (x+2)2

$x^3 + 3x^2 + 2x +4 = x^2 + 4x + 4\\ x^3 + 2x^2 -2x = 0\\ x(x^2 + 2x -2)=0\\ x=0\\ \vee$

$x^2 +2x -2=0\\ \Delta=2^2-4\cdot 1\cdot (-2) = 4 +8=12\\ \sqrt{\Delta}=\sqrt{12}=2\sqrt3\\ x=\frac{-2-2\sqrt3}{2}=-1-\sqrt3\\ x=\frac{-2+2\sqrt3}{2}=-1+\sqrt3$

4 votes Thanks 4

lapik

x³+3x²+2x+4=(x+2)²

x³+3x²+2x+4=x²+4+4x

x³+2x²-2x=0

x(x²+2x-2)=0

x²+2x-2=0 lub x=0

a=1

b=2

c=-2

Δ=b²-4ac

Δ=2²-4·1·(-2)=4+8=12

√Δ=2√3

x₁=2√3-2/2=√3-1

x₂=-2√3-2/2=-√3-1

x=-√3-1 lub x=0 lub x=√3-1

2 votes Thanks 5

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