Question

The sum of the square of two consecutive whole number is 25. Find the numbers

Answer 1

Don't you mean "the sum of the squares ..."?
The sum of the squares of two consecutive whole numbers is 25.  Find the numbers.  Let the first be represented by x and the second by x+1.
Then x^2+(x+1)^2=25.  Expanding, x^2+x^2+2x+1=25.
Rewriting this as a quadratic equation in standard form,

2x^2+2x+1=25, or 2x^2+2x-24=0.  Simplifying, x^2+x-12=0.
Factoring, (x-3)(x+4)=0.  Solving for x:  x-3=0, so x=3; x+4=0, so x=-4.
Choose the positive x value:  x=3.  Then the next consecutive number is 2+1=3+1=4.

Check:  Does 3^2 + 4^2 = 5^2 = 25?  Yes.
The numbers are 3 and 4.