Difference between squares of two consecutive numbers is 59. What are the numbers?

The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The number are

If p is the difference between a number and its reciprocal and q is the difference between the square of the same number and the square of its reciprocal, then what is p⁴ + 4p² equal to ?

The sum of squares of two positive integers is 1025 and difference of their squares is 225. What percent is the difference of the numbers of their product?

The sum of digits of a 2-digit number is 12. When the digits are reversed, the number becomes greater by eighteen. What is the difference between the digits in the number ?

What are the two natural numbers whose product is 2400 and the sum of whose squares is 5200?