if x and y are positive real numbers such that x.[x] = 36 and y.[y] = 71,then x+y is equal to which number.[.]denotes the greatest integer function .
To find the value of x+y, we need to determine the values of x and y first.
Given that x.[x] = 36, where [x] denotes the greatest integer function, we know that the value of [x] should be the greatest integer less than or equal to x. Therefore, [x] = 6, as it is the greatest integer less than or equal to 6.
Now, we can write the equation x.[x] = 36 as x * 6 = 36. Solving for x, we find that x = 6.
Similarly, for y.[y] = 71, we can deduce that the value of [y] should be 10, as it is the greatest integer less than or equal to 10.
Substituting this in the equation y * 10 = 71, we find that y = 71/10.
Finally, we can find the value of x + y by substituting the determined values:
x + y = 6 + 71/10
To add the fractions, it is convenient to express them with a common denominator:
x + y = 60/10 + 71/10 = (60 + 71)/10 = 131/10.
Therefore, x + y is equal to 131/10.
To find the value of x+y, we need to determine the values of x and y from the given conditions.
Let's first understand how the greatest integer function works. The greatest integer function, denoted as [x], takes a real number x and assigns the greatest integer less than or equal to x. For example, [3.8] = 3 and [5.2] = 5.
From the given equation x.[x] = 36, we can see that multiplying x with [x] gives us 36. Since [x] is the greatest integer less than or equal to x, it means that [x] is a whole number. We need to find a whole number [x] such that x multiplied by that whole number equals 36.
To find the value of [x], we can list down possible whole number values from the smaller side and try multiplying them with x until we find the one that gives us 36. Let's try it:
For [x] = 1: x * 1 = 36 (Not equal to 36)
For [x] = 2: x * 2 = 36 (Not equal to 36)
For [x] = 3: x * 3 = 36 (Not equal to 36)
For [x] = 4: x * 4 = 36 (Not equal to 36)
For [x] = 5: x * 5 = 36 (Not equal to 36)
For [x] = 6: x * 6 = 36 (Equal to 36)
So, we found that [x] = 6 and x = 36/6 = 6.
Now, let's move on to the second equation y.[y] = 71. Similarly, we need to find the value of [y] such that y multiplied by that whole number equals 71.
We can follow the same steps as above to find [y]. Let's try it:
For [y] = 1: y * 1 = 71 (Not equal to 71)
For [y] = 2: y * 2 = 71 (Not equal to 71)
For [y] = 3: y * 3 = 71 (Not equal to 71)
For [y] = 4: y * 4 = 71 (Not equal to 71)
For [y] = 5: y * 5 = 71 (Not equal to 71)
For [y] = 6: y * 6 = 71 (Not equal to 71)
For [y] = 7: y * 7 = 71 (Equal to 71)
So, we found that [y] = 7 and y = 71/7 = 10.142857... (approximately).
Finally, we need to find the value of x+y. Plugging in the values of x and y:
x + y = 6 + 10.142857...
x + y ≈ 16.142857...
Therefore, x+y is approximately equal to 16.142857.
how about an example of x.[x] ? For instance, if x=15.72, does that make
x.[x] = 15.72.15?
Not sure what's happening here. If x is an integer, the [x] = x
Or is x.[x] == x*[x]?
If so, then using the decimal point as an operator is just confusing.