Respostas

2014-07-15T18:22:07-03:00
A)(x²+1)²+50=15(x²+1) 
x^4+2x²+1+50=15x²+15 
x^4-13x²+51-15=0 
x^4-13x²+36=0 
x²=y 
y²-13y+36=0 
∆=(-13)²-4(1)(36)= 
25=5 
y=(13±5)/2 
y'=8/2=4 
y"=18/2=9 
mas y=x² 
x²=4 
x=√4 
x=±2 
x²=9 
x=√9 
x=±3 
solução 
(-2,2,-3,3)

b) (2x²-5)²=10(2x²-5)+39 
4x^4-20x²+25 = 10x²-50+39 
4x^4-20x²-10x²+25+50-39 =0 
4x^4-30x²+36=0 
x²=y
4y²-30y+36=0
Δ= (-30)²-4(4)(36)
Δ= 900-576
Δ= 324
y= (-30±√324)/2.4
y= -30±18/8
y'= -30+18/8 = -12/8 = 3/2
y"= -30-18/8 = -48/8 = -6
mas, y=x²
x²= 3/2
x'= √3/2
x²= -6
x"= -√6

c) x^4+6x²+9-19x²-57+84 =0
x^4-13x²+36 =0
x²=y
y²-13y+36 =0
Δ= (-13)²-4(1)(36)
Δ= 169-144
Δ= 25
y= -(-13)±√25/2.1
y= 13
±5/2
y'= 18/2 = 9
y"= 8/2 = 4
mas, x²=y
x²= 9
x= 
√9
x'= 3
x²= 4

x= 
√4
x"= 2
2 3 2