Решение задания приложено
Вот! просто решаешь через дискриминант)))
Я не знаю но считаю будет так
4X^4 - 11X^2 + 6 = 0
X^2 = A ; A > 0
4A^2 - 11A + 6 = 0
D = 121 - 96 = 25 ;√ D = 5
A1 = ( 11 + 5 ): 8 = 2
A2 = ( 11 - 5 ) : 8 = 3/4
X^2 = 2
X1 = √ 2
X2 = - √ 2
X^2 = 3/4
X3 = ( √ 3 ) / 2
X4 = - ( √ 3 ) / 2
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( 5 / (X^2 + 1 )) + ( 3 / X^2 + 6 ) = 7/10
X^2 + 1 ≠ 0 ; X^2 + 6 ≠ 0
5 * 10 * ( X^2 + 6 ) + 3 * 10 * ( X^2 + 1 ) = 7 * ( X^2 + 1 ) * ( X^2 + 6 )
50X^2 + 300 + 30X^2 + 30 = 7 * ( X^4 + 6X^2 + X^2 + 6 )
80X^2 + 330 = 7 * ( X^4 + 7X^2 + 6 )
80X^2 + 330 = 7X^4 + 49X^2 + 42
7X^4 + 49X^2 - 80X^2 + 42 - 330 = 0
7X^4 - 31X^2 - 288 = 0
X^2 = A ; A > 0
7A^2 - 31A - 288 = 0
D = 961 + 8064 = 9025 ; √ D = 95
A1 = ( 31 + 95 ) : 14 = 9
A2 = ( 31 - 95 ) : 14 = - 64/14 ( < 0 )
X^2 = 9
X1 = + 3
X2 = - 3
Ctg2x = 0
2x = pi/2 + pik /:2
x = pi/4 + (pik)/2, k ∈ Z