Problema Solution

The sum of the squares of two positive numbers is 808. One number is four more than the other. Find the two numbers. The sum of a number and its reciprocal is 106/45. Find the number.

Answer provided by our tutors

x^2+y^2=808

x=y+4

substitute the value of x in the equation

(y+4)^2+y^2=808

y^2+8y+16+y^2=808

2y^2+8y-792=0

/2

y^2+4y-396=0

y^2+22y-18y-396=0

y(y+22)-18(y+22)=0

(y+22)(y-18)=0

y=-22 OR 18 

x=-18 OR 22 

(-18,-22), (18,22)