LAST YEAR BOB'S AGE WAS A SQUARE NUMBER AND NEXT YEAR IT WILL BE A CUBE NUMBER. HOW OLD IS BOB NOW ? PLEASE EXPLAIN HOW YOU WORK IT OUT ,THANKS
make a list of squares:
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 ..
and a list of cubes
1 8 27 64 225 ..
which of these are 2 apart ? (next year - last year = 2)
look like 25 and 27
So last year he was 25 and next year he will be 27
Ook
Thx
Erm 😕
To find out Bob's current age, we need to consider that his age last year was a square number and his age next year will be a cube number.
Let's start by assuming Bob's current age is x.
According to the given information, last year Bob's age was (x - 1) which is a square number.
Therefore, we can write the equation:
(x - 1) = n^2, where n is a positive integer.
Similarly, next year Bob's age will be (x + 1) which is a cube number.
So, we can write the equation:
(x + 1) = m^3, where m is a positive integer.
Now, we have a system of equations:
(x - 1) = n^2
(x + 1) = m^3
To find the solution, we can try different values for n and m until we find a pair of values that satisfies both equations.
Let's start with n = 2 and m = 2:
For n = 2, we have:
(x - 1) = 2^2
x - 1 = 4
x = 4 + 1
x = 5
For m = 2, we have:
(x + 1) = 2^3
x + 1 = 8
x = 8 - 1
x = 7
As you can see, when we substitute x = 5 and x = 7 into the equations, they don't satisfy both equations.
Let's continue trying different values until we find a solution.
For n = 3 and m = 2:
For n = 3, we have:
(x - 1) = 3^2
x - 1 = 9
x = 9 + 1
x = 10
For m = 2, we have:
(x + 1) = 2^3
x + 1 = 8
x = 8 - 1
x = 7
Again, substituting x = 10 and x = 7 into the equations does not satisfy both equations.
Let's continue trying.
For n = 5 and m = 3:
For n = 5, we have:
(x - 1) = 5^2
x - 1 = 25
x = 25 + 1
x = 26
For m = 3, we have:
(x + 1) = 3^3
x + 1 = 27
x = 27 - 1
x = 26
This time, when we substitute x = 26 into both equations, we find that it satisfies both equations. Therefore, Bob's current age is 26 years old.