Look at the following formula: 1 times 2 times 3 times 4 + 1, 2 times 3 times 4 times 5 + 1, 3 times 4 times 5 times 6 + 1, 4 times 5 times 6 times 7 + 1 Describe the characteristics of the above four formulas in language What kind of general conclusion can you guess? Please state the correctness of your conjecture
1) These four formulas are the product of four consecutive natural numbers plus 1
2) The sum of the product of four natural numbers plus 1 is a complete square number
3) If there are four natural numbers A-1, a, a + 1, a + 2, then
(a-1)a(a+1)(a+2) +1
= (a^2-1)(a^2+2a)+1
= a^4 + 2a^3 -a^2 -2a +1
= a^4 +2a^3 -2a^2 + a^2 -2a +1
= a^4 + 2a^2(a-1) + (a-1)^2
= (a^2+a-1)^2
Therefore, the conclusion of 2) is correct
What's the quotient of 32 times the sum of 15 and 8, and then divided by 6? What's the formula?
32×(15+8)÷6
=32×23÷6
=368/3
=122 2/3
It's 122 and two-thirds
0.6×(3.8-x)=1.5.
0.6×(3.8-x)=1.5,0.6×(3.8-x)÷0.6=1.5÷0.6, 3.8-x=2.5, 3.8-x+x=2.5+x, 2.5+x=3.8, 2.5+x-2.5=3.8-2.5, x=1.3.
How to make 120-6 = 114144 △ 24 = 6464-320 = 114 into a comprehensive formula
Wrong title? The last one should be 464-320 = 144
The formula is 120 - (464-320) △ 24 = 114
In an addition and subtraction formula, the sum of the subtracted, the subtracted and the difference is 114, and the difference is 18 times of the subtracted. So what is the difference?
Because: subtracted = subtracted + difference
So: subtracted = subtracted + difference = 114 / 2 = 57
Another: the difference is 18 times the subtraction
According to the sum multiple relation, the subtraction = 57 / (1 + 18) = 3
Then: difference = 3 * 18 = 54
How to list the simple formula of 372 + 86 + 114 + 28?
372+86+114+28
=(372+28)+(86+114)
=400+200
=600
11 + 1 + 1-111 = 4 move one of the matches to make it the correct formula
114+1-111=4
Use a matchstick to make 1 + 11 + 111 = 4, move a matchstick to make the formula true
Put one of 11 in the middle of 111
Become 1 + 1 + 1 + 1 = 4
The equation holds
Formula 111 + 11 + 1 = 4 move a match to make the formula hold
11+11+1≠4
1+1+1+1=4
74-4 = 4 how to move one of the matches to make the formula hold
7 + 1-4 = 4 remove one of the "4" matches of "74" to make "4" become "+" put the removed match behind "+"