Determinar a e b, de modo que os pares ordenados a seguir sejam iguais:
a) (2a-2, b+3) e (3a+5, 2b-7)
b) (2a, a-8) e (1-3b, b)
c) (a²+a, 2b) e (6, b²)
d) (b², |a|) e (4, 3)
a) (2a-2, b+3) e (3a+5, 2b-7)
b) (2a, a-8) e (1-3b, b)
c) (a²+a, 2b) e (6, b²)
d) (b², |a|) e (4, 3)
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a) (2a-2, b+3) e (3a+5, 2b-7)
2a-2 = 3a+5==> 3a -2a = -2-5==> a = - 7
b+3 = 2b-7==> 2b-b = 3+7 ==> b = 10
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b) (2a, a-8) e (1-3b, b)
2a = 1-3b ==> 2a +3b = 1
a-8 = b ==> a = b + 8
2a +3b = 1
a = b + 8
2(b + 8) + 3b = 1 ==> 2b+16+3b = 1 ==> 5b = 1-16==> 5b = - 15 ==> b = - 3
a = b + 8 ==> a = - 3 + 8 ==> a = 5
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c) (a²+a, 2b) e (6, b²)
a²+a = 6
a²+a - 6 = 0
a = 1² -4.1.(-6) = 1 + 24= 25
a= -1+/-√25 ==> a = - 1+/-5
2.1 2
a1= -1+5 ==> a1 = 2
2
a2= -1-5 ==> a2 = - 3
2
2b = b²
b² - 2b = 0
b(b-2) = 0
b1 = 0
b2 - 2 = 0
b2 = 2
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d) (b², |a|) e (4, 3)
b² = 4 ==> b = +/- √4 ==> b = +/- 2
|a| = 3 ==> a = +/- 3