Question

giải phương trình |x+10|⁵ +|x-10|⁵=200000

Answer 1

Làm nhầm làm lại nhé

Ta có:

|x + 10|⁵ + |x - 10|⁵

= |x + 10|⁵ + |10 - x|⁵

= |x⁵ + 50x⁴ + 1000x³ + 10000x² + 50000x + 100000| + |-x⁵ + 50x⁴ - 1000x³ + 10000x²​ - 50000x + 100000|

\(\ge\)|100x⁴ + 20000x² + 200000|

\(\ge\)|200000| = 200000

Dấu = xảy ra khi x = 0

Answer 2

Ta có:

|x + 10|⁵ + |x - 10|⁵

= |x + 10|⁵ + |10 - x|⁵

= |x⁵ + 50x⁴ + 1000x³ + 10000x² + 50000x + 1000000| + |-x⁵ + 50x⁴ - 1000x³ + 10000x²​ - 50000x + 1000000|

\(\ge\)|100x⁴ + 20000x² + 2000000|

\(\ge\)|2000000| = 2000000

Dấu = xảy ra khi x = 0