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the sum of two numbers is 19 and the sum of their squares is 205.find the numbers.

Sagot :

x + y = 19 --->> can be written as y = 19-x
x^2 + y^2 = 205
[tex]x^2 + (19-x)^2 = 205[/tex]
[tex]x^2 + 361 - 38x + x^2 = 205[/tex]
[tex]2x^2 - 38x + 156 = 0[/tex]
x=13
x=6

Therefore the solution is:
1) x= 13, y=6
or
2) x=6, y=13