Решить систему уравнений

Объяснение:

y2 = 10 - 2x4

x2 + 2(10 - 2x4) = 15

x2 + 20 - 4x4 = 15

x2 = t

t + 20 - 4t2 = 15

4t2 - t - 5 =0

D = 1 + 80 = 81

t =  1 - 9 / 8 = - 1

T = 1 + 9/ 8 = 10 / 8 = 5/4

x2 = t ;   =>     x2 =  5/4 ;  =>  x = sqrt(5/4)

5/4 + 2y2 = 15

2y2 = 13,75

y2 = 6,8725    => y = sqrt(6,8725)

2x^4 + y^2 = 10 |*2

x^2 + 2y^2 = 15

вычитаем 2 из 1

4x^4 + 2y^2 - x^2 - 2y^2 = 20 - 15

4x^4 - x^2 - 5 = 0

x^2 = t >= 0

4t^2 - t - 5 = 0

D = 1 + 80 = 81

t12 = (1 +- 9)/8 = -1   5/4

t1 = -1 нет < 0

t2 = 5/4

x^2 = 5/4

x = +- √5/2

5/4 + 2y^2 = 15

2y^2 = 60/4 - 5/4 = 55/4

y^2 = 55/8

y = +- √(55/8)

ответ (+- √5/2, +- √(55/8)) все комбинации