11. (i) Write a pair of integers whose
(a) sum is -7
(b) difference is -10
Answers
Answer:
We want to find out the number of integers of the form 5x11 if x is an odd integer and 0<x>50.
If 5x11 is an integer, then the numerator has to be a multiple of 11.
Since 5 is not a multiple of 11, it is necessary that x is a multiple of 11.
Since x is an odd integer, it has to be an odd multiple of 11.
⇒x=(2n+1)11,n∈Z, if there are no restcitions on the value of x.
However, there is a restriction that 0<x>50. This means that 0 is lesser than x and at the same time x is greater than 50.
The values of x which are lesser than 50 are those which correspond to n≤1. These are to be excluded from our list.
So we change 2n+1 to 2n+3 and for natural numbers n.
⇒x=(2n+3)11,n∈N.
It can be seen that there are infinite values of x meeting this requirement.
The restriction 0<x>50 can possibly be a typographical error since the part 0<x is superfluous.
If the restriction is 0<x<50 the values of x that satisfy the requirements are 11 and 33 and thus we get two integers of the form 5x11 i.e. 5 and 15 which meet our requirement.
Same thing in this sum ............
the full explanation of our sun
learn .....
-5+ (+2)= -7
-5 - (+2)= -10