One number is 1 more than twice another number. The sum of the squares of the two numbers is 97. Find the numbers.

Answer 1

Let y= 1+2x and x² +y² =97 then x² + (1+2x)² =97 so x² + 1 +4x + 4x² =97 and 5x² +4x +1 +97

now 5x² +4x -96 =0. Use the quadratic formula where b=-4 b²=16 and 4ac = 1920 where a = 5 and c=96.

So x=(-4±√(16 +1920))/10 and x= (-4± 44)/10 and x= 4. Hence y =9.