tolong bantu saya jawab !
Answer (4)
( 15 − x )! = [ 15 − ( x + 2 )]! × [ 15 − ( x + 1 )] × ( 15 − x ) = ( 15 − x − 2 )! × ( 15 − x − 1 ) × ( 15 − x ) = ( 13 − x )! × ( 14 − x ) × ( 15 − x ) = ( 13 − x )! × ( 210 − 14 x − 15 x + x 2 ) = ( 13 − x )! × ( x 2 − 29 x + 210 ) t h ere f ore : ( 13 − x )! ⋅ 2 ! ( 15 − x )! = ( 13 − x )! ⋅ 2 ! ( 13 − x )! ⋅ ( x 2 − 29 x + 210 ) = 2 x 2 − 29 x + 210
x ! = ( x − 2 )! × ( x − 1 ) × x = ( x − 2 )! × ( x 2 − x ) t h ere f ore : ( x − 2 )! ⋅ 2 ! x ! = ( x − 2 )! ⋅ 2 ( x − 2 )! ⋅ ( x 2 − x ) = 2 x 2 − x ====================================== 2 x 2 − 29 x + 210 = 2 x 2 − x ∣ m u lt i pl y b o t h s i d es b y 2 x 2 − 29 x + 210 = x 2 − x x 2 − x 2 − 29 x + x = − 210 − 28 x = − 210 ∣ d i v i d e b o t h s i d es b y ( − 28 ) x = 7.5 ∈ / Z
T hi s e q u a t i o n ha s n o t so l u t i o n b ec a u se x m u s t b e an in t e g er ! x ∈ \O
( 13 − x )! ⋅ 2 ! ( 15 − x )! = ( x − 2 )! ⋅ 2 ! x ! 2 ( 14 − x ) ( 15 − x ) = 2 ( x − 1 ) x ( 14 − x ) ( 15 − x ) = ( x − 1 ) x 210 − 14 x − 15 x + x 2 = x 2 − x 28 x = 210 x = 28 210 = 7.5
The factorial is defined for natural numbers and since 7.5 isn't one, this equation has no solutions.
The equation provided simplifies to finding X, which results in X = 7.5 . Since the factorial function requires non-negative integers, there is no valid integer solution for X. Thus, the equation has no integer solution.
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