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 solve for x and y separately and then add them together.
Given that x.[x] = 36 and y.[y] = 71, we know that [x] is the greatest integer less than or equal to x, and [y] is the greatest integer less than or equal to y.
Let's start by solving for x. We know that x.[x] = 36. This means that x multiplied by the greatest integer less than or equal to x equals 36.
To find x, we can use trial and error. We know that x is a positive real number, so we can start by substituting different positive real numbers for x until we find one that satisfies the equation. We can try values like 1, 2, 3, and so on, until we find the correct value.
Let's try x = 6. When we substitute x = 6 into the equation x.[x] = 36, we get 6.[6] = 36. The greatest integer less than or equal to 6 is 6 itself, so the equation becomes 6.6 = 36, which is not true. So, 6 is not the correct value for x.
Let's try x = 7. When we substitute x = 7 into the equation x.[x] = 36, we get 7.[7] = 36. The greatest integer less than or equal to 7 is 7 itself, so the equation becomes 7.7 = 49, which is not true. So, 7 is not the correct value for x.
Let's continue this process until we find the correct value for x.
Now let's solve for y using the same approach. We know that y.[y] = 71. This means that y multiplied by the greatest integer less than or equal to y equals 71.
We can use trial and error again to find the value of y. Let's try the same values we tried for x and see if any of them satisfy the equation.
By trying different positive real numbers for y, we find that y = 8 satisfies the equation y.[y] = 71. When we substitute y = 8 into the equation, we get 8.[8] = 71. The greatest integer less than or equal to 8 is 8 itself, so the equation becomes 8.8 = 64, which is not true.
Therefore, none of the positive real numbers we have tried so far satisfy the equation y.[y] = 71.
Since we couldn't find the correct values for x and y, we cannot determine the value of x+y.
In summary, to find the value of x+y, we need the correct values for x and y which satisfy the given equations x.[x] = 36 and y.[y] = 71. However, after trying different positive real numbers, we couldn't find the correct values. Hence, we cannot determine the value of x+y.