If an integer is both a square and a cube, it can be of the form:
<span>(<span>a3</span><span>)^2</span></span>
Now,
since a cube can be of the form 7k or 7k+-1(thanks to FoolForMath),
we write
<span><span>a^3</span>=7k</span>
and get the no to be
49k^2
, which is in the form of 7 times something
<span>49<span>k^2</span>=7×(7<span>k^2</span>)</span>
Now put
<span><span>a^3</span>=7k+−1</span>
Square it
and you'll get a number in the form of (7times something +1)
Answer:
499/999
Step-by-step explanation:
The decimal number written is:
0.499...
Such that these 3 decimals are repeated as:
0.499499499...
Let's define this number as k
k = 0.499...
Let's multiply this number by 1000 (the same number of zeros as important decimals after the decimal point)
we get:
1000*k = (1000)*(0.499...) = 499.499...
Now we can subtract the original number k, so we get:
1000*k - k = 499.499... - 0.499...
In this way, we remove the part after the decimal point:
1000*k - k = 499.499... - 0.499...
(1000 - 1)*k = 499
999*k = 499
Now we can divide both sides by 999
(999*k)/999 = 499/999
k = 499/999
The fraction notation of our number is 499/999 (and this is the simplest form)
Answer:
25/100
Step-by-step explanation:
(9x - 7) - (5x + 10 )
2x - 15x
- 13x