Question

Resolva as equações biquadradas (com cálculo
${x}^{4} - 5 {x}^{2} + 4 = 0$
${x}^{4} + 2x {}^{2} + 7 = 0$
$2 {x}^{4} - x {}^{2} - 15 = 0$
$8 {x}^{4} + 7 {x}^{2} + 5 = 0$
$4 {x}^{4} - 5 {x}^{2} + 1 = 0$
$2x^{4} - 3 {x}^{2} - 20 = 0$
${x}^{4} + 3 {x}^{2} = 4$
$5 {x}^{4} = 3 {x}^{2} - 8$
$x^4 + 4 = - 5 {x}^{2}$
$4 {x}^{4} + 4 = 17 {x}^{2}$
$x^{4} - 25 {x}^{2} = 0$
$x {}^{4} - 9 = 0$
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Answer 1

a) x⁴-5x²+4=0

(x²)²-5x²+4=0

x²=k

k²-5k+4=0

∆=25-16=9

k=(5±3)/2

k'=(5+3)/2=8/2=4

k"=(5-3)/2=2/2=1

x²=4

x=±√4 =±2

x²=1

x=±√1=±1

s={-2,-1,1,2}

b) x⁴+2x²+7=0

(x²)²+2.x²+7=0

x²=y

y²+2y+7=0

∆=4-28=-24<0

S=∅

c) 2x⁴-x²-15=0

2(x²)²-x²-15=0

x²=m

2m²-m-15=0

∆=1+120=121

m=(1±11)/4

m'=(1+11)/4 =12/4=3

x²=3

x=±√3

S={-√3,√3}