((10)1÷2 ) +((7)3÷6)+((5)4÷5)-((8)4÷7)
Answers
z=f(x,y)=x+y , where + is not addition operator
Given, 2+3=8, 3+7=27, 4+5=32,5+8=60, 6+7=72
Find, 7+8= ?
From the given example, we can be sure that + is not a mere addition operator.
Taking 2+3=8, if + is multiplication operator then, 2⋅3=6, which is 2 less than 8 so to adjust we add 2,
f(2,3)=2+3=2⋅3+2=2⋅(3+1)=8
So we can assume our definition as f(x,y)=x+y=x⋅(y+1)
f(3,7)=3⋅(7+1)=3⋅8=24, but this is 3 less to 27.
i.e, f(3,7)=3⋅(7+1)+3=3⋅(7+1+1)=3⋅(7+2)=27
So from this we can understand that there is some kind of progression is carried out with the constant in f(x,y)=x⋅(y+1),
Therefore re-writing out definition as, f(x,y)=x+y=x⋅(y+c), where is c is a constant of unknown behavior.
Again taking our first given statement and the knowledge of solving two terms we have,
2+3=8 which is nothing but 2⋅(3+1)=2⋅4=8
3+7=27which is 3⋅(7+2)=3⋅9=27
4+5=32is 4⋅(5+3)=4⋅8=32
Similarly,
5+8=60 is 5⋅(8+4)=5⋅12=60, and
6+7=72 is 6⋅(7+5)=6⋅12=72
Which satisfies all the given hence, we can conclude that,
7+8=7⋅(8+6)=7⋅14=98.
In general, we have
z=f(x,y)=x+y=x⋅(y+c), where c is denotes the term number in the series with 1st term as 2+3=8, 2nd term as 3+7=27 and so on.