I need help regarding the following question:
Four different integers are in A.P. One of these integers is equal to the squares of the rest integers. Find the numbers.
It is like this:
If a, b, c, d are in A.P. then d=a^2 +b^2 +c^2
I know the answer, but I simply can't figure out the explanation. The A.P. is -1,0,1,2
But I do not understand how it came.
Any help will be appreciated.
Did you mean sum of squares of the rest of the integers? Taking that to be what you meant, begin by writing relevant equations to the problem.
b-a=c-b
2b=a+c --- 1
d-c=c-b
2c=b+d
b=2c-d --- 2
Sub 2 into 1, 2(2c-d)=a+c
a=3c-2d -- 3
--- 4
Substitute 3 and 2 into 4
After simplifying, you are left with
Then let c be 0(you could have picked d to be 0), then solve for d and the rest of the unknowns.