Question

Решите уравнениях^4-7х^2+12=0х^4-11х^2+18=0

Answer 1

X^4 - 7X^2 + 12 = 0 
----------------------
X^2 = A ( A > 0 ) 
A^2 - 7A + 12 = 0
D = 49 - 48 = 1 ; √ D = 1 
A1 = ( 7 + 1 ) : 2 = 4 
A2 = 6 : 2 = 3 
----------------
X^2 = A 
-----------
X^2 = 4 
X1 = 2 
X2 = ( - 2 ) 
----------
X^2 = 3 
X3 = √ 3 
X4 = - √ 3
===========
Уравнение 2 
X^4 - 11X^2 + 18 = 0
---------
X^2 = A ( A > 0 )
A^2 - 11A + 18 = 0
D = 121 - 72 = 49 ; √ D = 7
A1 = ( 11 + 7) : 2 = 9 
A2 = 4 : 2 = 2 
-----------
X1 = 3
X2 = - 3 
X3 = √ 2
X4 = - √ 2