Ecuaciones de segundo grado (práctica)
2
Resuelve las siguientes ecuaciones de segundo grado x 2 −9 x +14=0 x= −(−9 ) ± √ (−9 ) 2 −4 ⋅ 1 ⋅ 14 2 ⋅ 1 x= 9 ± √ 81−56 2 = 9 ± √ 25 2 = 9 ± 5 2 x 1 = 9 +5 2 = 14 2 =7 ;x 2 = 9−5 2 = 4 2 =2 7 x 2 −21 x=0 x ( 7 x−21 ) =0 x 1 =0 x 2 ≡ 7 x− 21=0 ; 7 x=21;x= 21 7 =3 2 x 2 + 6 x+20 =0 x= −6 ± √ 6 2 −4 ⋅ 2 ⋅ 20 2 ⋅ 4 x= −6 ± √ 36−80 8 = −6 ± √ −44 8 ⇒∄ soluciones( raíz cuadradanúermo negativo ) 2 x 2 −18= 0 2 x 2 =18 ;x 2 = 18 2 ;x 2 =9 X=± √ 9=± 3 X 1 =3 ;X 2 =−3 x 2 − 7 x 2 =0 x ( x− 7 2 ) =0 x 1 =0 x 2 ≡x− 7 2 =0 ;x= 7 2 9 x 2 −6 x +1=0 x= −(−6 ) ± √ (−6 ) 2 −4 ⋅ 9 ⋅ 1 2 ⋅ 9
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Transcript of Ecuaciones de segundo grado (práctica)
Resuelve las siguientes ecuaciones de segundo grado
x2−9 x+14=0
x=−(−9 )±√ (−9 )2−4 ⋅1⋅ 14
2⋅1
x=9±√81−562
=9±√252
=9±52
x1=9+5
2=14
2=7 ; x2=
9−52
=42=2
7 x2−21 x=0x (7 x−21 )=0x1=0
x2≡7 x−21=0 ;7 x=21 ; x=217
=3
2 x2+6 x+20=0
x=−6±√62−4 ⋅2⋅ 202 ⋅4
x=−6±√36−808
=−6±√−448
⇒∄ soluciones(raíz cuadradanúermonegativo)
2 x2−18=0
2 x2=18 ;x2=182; x2=9
X=±√9=±3X1=3; X2=−3
x2−7 x2
=0
x (x−72 )=0
x1=0
x2≡ x−72=0 ; x=7
2
9 x2−6 x+1=0
x=−(−6 )±√ (−6 )2−4 ⋅9 ⋅1
2 ⋅9
x=6±√36−3618
=6±√018
=6±018
x1=6+018
= 618
=13; x2=
6−018
= 618
=13
x2+5x+6=0
x=−5±√52−4 ⋅1 ⋅62 ⋅1
x=−s ±√25−242
=−5±√12
=−5±12
x1=−5+1
2=−4
2=−2; x2=
−5−12
=−62
=−3
x2+4 x+3=0
x=−4 ±√42−4 ⋅1 ⋅32 ⋅1
x=−4 ±√16−122
=−4±√42
=−4±22
x1=−4+2
2=−2
2=−1 ; x2=
−4−22
=−62
=−3
7 x2−21 x=287 x2−21 x−28=0
x=−(−21 )±√(−21 )2−4 ⋅7 ⋅ (−28 )
2 ⋅7
x=21±√441+78414
=21±√122514
=21±3514
x1=21+35
14=56
14=4 ;x2=
21−3914
=−1414
=−1
