We know that x[x] = 36, which means x is between 6 and 7 (since 6[6] = 36 and 7[7] = 49). Let's set x = 6 + a, where a is the decimal part of x. Then we have:
x[x] = 6a = 36
a = 6
Therefore, x = 6.6
Similarly, y must be between 8 and 9 (since 8[8] = 64 and 9[9] = 81). Let's set y = 8 + b, where b is the decimal part of y. Then we have:
y[y] = 8b = 71
b = 8.875
Therefore, y = 8.875
So, x + y = 6.6 + 8.875 = 15.475. The greatest integer less than or equal to 15.475 is 15. Therefore, x + y = 15.
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.
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