Răspuns:
Explicație pas cu pas:
(m + 2)x^2 - 2(m - 1)x + m - 2 = 0
a)
m = 1
3x^2 + 2(1 - 1)x + 1 - 2 = 0
3x^2 - 1 = 0
3x^2 = 1
x^2 = 1/3
x1 = 1/√3 = √3/3
x1 = -√3/3
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m = 2
4x^2 - 2(2 - 1)x + 2 - 2 = 0
4x^2 - 2x = 0
2x^2 - x = 0
x(2x - 1) = 0
x1 = 0
2x - 1 = 0; 2x = 1; x2 = 1/2
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m = 0
2x^2 + 2x - 2 = 0
x^2 + x - 1 = 0
Δ = 1 + 4 = 5
x1 = (-1 + √5)/2
x2 = (-1 - √5)/2
_________________________
b)
(m + 2)x^2 - 2(m - 1)x + m - 2 = 0
x = 2
4(m + 2) - 4(m - 1) + m - 2 = 0
4m + 8 - 4m + 4 + m - 2 = 0
m + 10 = 0
m = -10
