Question

URGENT !VA ROG
Rezolvati in R ecuatia bipatrata
b) x^4+5x^2+4=0
c)2x^4-3x^2+1=0

Answer 1

c) Pentru a rezolva ecuatia bipatrata o "reducem" pana la forma ecuatiei de gradul ll : ax²+bx+c=0 prin inlocuirea lui cu alta necunoscuta:
Aici:
2x⁴-3x²+1=0
consideram x²=t
→2t²-3t+1=0
a=2
b=-3
c=1
∆=b²-4ac
∆=(-3)²-4*2*1=9-8=1

t1=(-b+√∆)/2a=( -(-3)+√1)/2*2=(3+1)/4=4/4=1

t2=(-b-√∆ )/2a=( -(-3)-√1)/2*2=(3-1)/4=2/4=½

Daca t=x², atunci rezolvam ecuatiile
x²=1 sau x²=½
√x²=√1 sau √x²=√½
|x|=1 sau |x|=√2/2
x=±1 sau x=±√2/2

S={±1; ±√2/2}

d) Aceeasi metoda:
x⁴+5x²+4=0
t=x²
→ t²+5t+4=0
a=1
b=5
c=4
∆=b²-4ac
∆=5²-4*1*4=25-16=9

t1=(-b+√∆)/2a=( -5+√9)/2*1=(-5+3)/2=-2/2=-1

t2=(-b-√∆)/2a=(-5-3)/2=-8/2=-4

→x²=-1 sau x²=-4
x=∅ 
S=∅

Answer 2

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