Dashanga agada a formulation of Agada tantra dealt in 3 Rd year bams agada tanta
Demonstração da Fórmula de Baskara
1. DEMONSTRAC¸ ˜AO DA F´ORMULA DE
BASKARA
Prof. Dr. Carlos A. P. Campani
COMPLETAC¸ ˜AO DE QUADRADOS
x2
+ bx = c
x2
+ bx +
b
2
2
= c +
b
2
2
x +
b
2
2
= c +
b2
4
Exemplo:
4x2
− 20x + 17 = 0
x2
− 5x +
17
4
= 0
x2
− 5x = −
17
4
x2
− 5x + −
5
2
2
= −
17
4
+ −
5
2
2
x −
5
2
2
= 2
x −
5
2
= ±
√
2
x =
5
2
±
√
2
1
2. DEMONSTRAC¸ ˜AO
ax2
+ bx + c = 0
ax2
+ bx = −c
x2
+
bx
a
= −
c
a
x2
+
bx
a
+
b
2a
2
= −
c
a
+
b
2a
2
[completa¸c˜ao de quadrados]
x +
b
2a
2
= −
c
a
+
b2
4a2
x +
b
2a
2
=
−4ac + b2
4a2
x +
b
2a
= ±
b2 − 4ac
4a2
x = −
b
2a
±
√
b2 − 4ac
2a
x =
−b ±
√
b2 − 4ac
2a
2