Question

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Answer 1

(x^2+2)^2=2(x^2+2)
x^4+4x^2+4=2x^2+4
x^4+4x^2-2x^2+4-4=0
x^4+2x^2=0

x^2=x

(x^2)^2+2x^2=0
x^2+2x=0
x(x+2)=0
x= -2

b)
x^4+16x^2=0

x^2= x

(x^2)^2+16x^2=0
x^2+16x=0
x(x+16)=0
x= -16


2)
a)
4x^4-9x^2+2=0

x^2=x

(4x^2)^2-9x^2+2=0
4x^2-9x+2=0

b)
4x^2-9x+2=0
∆= b^2-4.a.c
∆= (-9)^2-4.4.2
∆= 81-32
∆=49
x= -b+-√∆
---------------
___2.a

x= -(-9)+√49
-------------------
_____2.4

x= +9+7
-------------
___8

x= 16/8
x'= 2

x"= +9-7
-------------
____8

x"= 2/8

x"= 1/4


3)
a)
(y^2-4)^2+2.(y^2+5)^2=66
y^4-8y^2+16+2.(y^4+10y^2+25)=66
y^4-8y^2+16+2y^4+20y^2+50=66
y^4+2y^4-8y^2+20y^2+16+50-66=0
3y^4+12y^2+66-66=0
3y^4+12y^2=0