Inductive or detuctive? The following equations show that n2 - n + 11 is a prime number for all counting numbers n = {1, 2, 3, 4, } n = 1 (1)2 - 1 + 11 = 11 n = 2 (2)2 - 2 + 11 = 13 n = 3 (3)2 - 3 + 11 = 17 n = 4 (4)2 - 4 + 11 = 23

47 - 90 = 43

43 - 180 = x

x = 137

step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

radha is now 5 years old

3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

hope this !