Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
2√72 / √8 ± √2
If the denominator is √8 + √2,
2√72 / √8 + √2
= 2√(2*2*2*3*3) / √(2*2*2) + √2
= 2*2*3√2 / 2√2 + √2
= 12√2 / 3√2
= 4
Answer:mn jjjjjjjjjjjjjjjjjjjjjjjj,uyhhhbgfvStep-by-step explanation:
Omg, im so sorry, i was moving and put my books on top of my keyboard it did this. Sorry. SOMEBODY DELETE THIS PLEASE. Sorry again.
Answer:
-3,-4,-5
Step-by-step explanation:
those are all numbers less than -2! your welcome! please give me brainliest!
Answer:
Step-by-step explanation:
twice a number .....multiplication
decreased by 4.....subtraction
divided by 8.....division
addition is missing <====
although, twice a number could also be addition.....but I have never used it for addition
lets say ur number is 4.......twice the number 4 could be : 2 * 4 or 4 + 4
