The sum of the squares of two natural numbers is 410. If the squares of the large number is 26 times the smaller number plus 3, then the difference between the two numbers is

Correct option is C

Let's denote the larger number as x and the smaller one as y.

According to question
x^2 + y^2 = 410
x^2 = 26y + 3
Substituting the second equation into the first, we get:

26y + 3 + y^2 = 410

Rearranging the equation, we have a quadratic equation:

y^2 + 26y - 407 = 0

Solving this quadratic equation, we find that y = 7 or y = -57.

Since y is a natural number, we discard the negative solution. Therefore, y = 7.

Substituting y = 7 into the second equation, we get:

x^2 = 26 * 7 + 3 = 185

Taking the square root of both sides, we get x = 13 or x = -13.

Again, since x is a natural number, we discard the negative solution. Therefore, x = 13.

The difference between the two numbers is x - y = 13 - 7 = 6.

Therefore, the difference between the two numbers is 6.