Melchor Bernabé Gustavo. Semana 6

1.----3x^ 2−5x+2=0

−(−5) ± √−5^ 2 − 4(3)(2)/2(3)

x = 5 ± √25 − 24/6 

x = 5 ± √1/6 

x1 = 5 + 1/6 = 6/6 = 1 

x2 = 5 − 1/6 = 4/6 = 2/3 

4.----49x^ 2 −70x +25 = 0 

𝑥 = − ( −70 ) ± √ ( −70 )^ 2 − 4 (49 ) (25 )/ 2 (49 )

𝑥 = − ( −70 ) ± √4900 − 4900/ 2 (49 ) 

𝑥 = 70 ± √ 0/98

𝑥 = 70/98 = 10/14 = 5/ 7   

2.---- 32x^ 2 +18x −17 = 0 

𝑥 = − 1 8 ± √18^ 2 − 4 (32 ) ( −17 )/2(32 )

𝑥 = −18 ± √ 324 − 2176 /64 

𝑥 = − 18 ± √2500/64

𝑥 = − 1 8 ± 50/64

𝑥 1 = − 18 + 50/64 = 32/64 = 1/2

𝑥 2 = − 1 8 − 50/64 = − 68/64 = − 17/16 

5.----105 = x +2x^2 

Corrección. - 2x^ 2 + x −105 = 0

𝑥 = − 1 ± √ 1^ 2 − 4 ( 2 ) ( −105 ) /2( 2 )

𝑥 = − 1 ± √ 1 − 840/4

𝑥 = − 1 ± √841/4

𝑥 = − 1 ± 29/4   

𝑥 1 = − 1 + 29/4 = 28/4 = 7

𝑥 2 = − 1 − 29/4 = −30/4 = − 15/2

3.----x^2 +11x = −24 

Corrección. - x^ 2+11x+24=0

x = − ( −11 ) ± √11^2 − 4 ( 1 ) (24 )/2( 1 )

x = − ( −11 ) ± √121 − 96/2

x = −11 ± √ 5/2 

x = − 1 1 ± 5/2

x1 = −11 ± 5/2 = − 6/2 = − 3

x2 = −11 − 5/2 = −16/2 = − 8 

𝑥 = − ( −12 ) ± √ (12 )^ 2 − 4 ( − 7 ) (64 ) /2( − 7 ) 

𝑥 = 12 ± √144 − 1792/−14 

𝑥 = −12 ± √1936/−14

𝑥 = −12 ± 44/−14  

𝑥 1 = −12 +44/−14 = 32/−14 = = 16/7

𝑥 2 = −12 −44/−14 = −56/−14 = 4