Решите уравнения : х^4-13х^2+36=0 и х^ 4-65х^2+64=0

Question

Решите уравнения :
х^4-13х^2+36=0
и
х^ 4-65х^2+64=0

Answer 1

1) x^4 - 13x^2 + 36 = 0;
 x^2 = t ≥0;
t^2 - 13 t + 36 = 0;
D = 169 - 144 = 25 = 5^2;
 t1 = 9 ; ⇒ x^2 = 9; x = + - 3;
 t2 = 4; ⇒ x^2 = 4 ; x = + - 2.
2) x^4 - 65 x^2 + 64 = 0;
 x^2 = t ≥ 0 ;
 t^2 - 65 t + 64 = 0;
 t1 = 1; ⇒ x^2 = 1 ;   x = + - 1;
 t2 = 64; ⇒ x^2 = 64 ; x = + - 8

Comments

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