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Sagot :
1) x^2 + 2x - 24 = 0
Delta^2 = (2)^2 - 4*1*(-24)
Delta^2 = 4 + 96
Delta^2 = 100
Delta = V100
Delta = 10 > 0 donc 2 solutions
X1 = (-2-10)/2 = (-12)/2=(-6)
X2 = (-2+10)/2 = 8/2 = 4
2) 2x(x+3)=5x+6
2x^2 + 6x - 5x - 6 = 0
2x^2 + x - 6 = 0
Delta^2 = (1)^2 - 4*2*(-6)
Delta^2 = 1 + 48
Delta^2 = 49
Delta = V49
Delta = 7 > 0 donc 2 solutions
X1 = (-1-7)/(2*2)
X1 = (-8)/4
X1 = (-2)
X2 = (-1+7)/(2*2)
X2 = 6/4
X2 = 3/2
3) 2x^2 = 2x + 1
2x^2 - 2x - 1 = 0
Delta^2 = (-2)^2 - 4*2*(-1)
Delta^2 = 4 + 8
Delta^2 = 12
Delta = V12
Delta = 2V3 > 0 donc 2 solutions
X1 = (2-2V3)/(2*2)
X1 = (1-V3)/2
X2 = (2+2V3)/(2*2)
X2 = (1+V3)/2
4) 1 - x(7x+3) = -189
1 - 7x^2 - 3x = - 189
7x^2 + 3x - 189 - 1 = 0
7x^2 + 3x - 190 = 0
Delta^2 = (3)^2 - 4*7*(-190)
Delta^2 = 9 + 5320
Delta^2 = 5329
Delta = V5329
Delta = 73 > 0 donc 2 solutions
X1 = (-3-73)/(2*7)
X1 = (-76)/14
X1 = (-38/7)
X2 = (-3+73)/(2*7)
X2 = 70/14
X2 = 5
Delta^2 = (2)^2 - 4*1*(-24)
Delta^2 = 4 + 96
Delta^2 = 100
Delta = V100
Delta = 10 > 0 donc 2 solutions
X1 = (-2-10)/2 = (-12)/2=(-6)
X2 = (-2+10)/2 = 8/2 = 4
2) 2x(x+3)=5x+6
2x^2 + 6x - 5x - 6 = 0
2x^2 + x - 6 = 0
Delta^2 = (1)^2 - 4*2*(-6)
Delta^2 = 1 + 48
Delta^2 = 49
Delta = V49
Delta = 7 > 0 donc 2 solutions
X1 = (-1-7)/(2*2)
X1 = (-8)/4
X1 = (-2)
X2 = (-1+7)/(2*2)
X2 = 6/4
X2 = 3/2
3) 2x^2 = 2x + 1
2x^2 - 2x - 1 = 0
Delta^2 = (-2)^2 - 4*2*(-1)
Delta^2 = 4 + 8
Delta^2 = 12
Delta = V12
Delta = 2V3 > 0 donc 2 solutions
X1 = (2-2V3)/(2*2)
X1 = (1-V3)/2
X2 = (2+2V3)/(2*2)
X2 = (1+V3)/2
4) 1 - x(7x+3) = -189
1 - 7x^2 - 3x = - 189
7x^2 + 3x - 189 - 1 = 0
7x^2 + 3x - 190 = 0
Delta^2 = (3)^2 - 4*7*(-190)
Delta^2 = 9 + 5320
Delta^2 = 5329
Delta = V5329
Delta = 73 > 0 donc 2 solutions
X1 = (-3-73)/(2*7)
X1 = (-76)/14
X1 = (-38/7)
X2 = (-3+73)/(2*7)
X2 = 70/14
X2 = 5
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