Question 36351: The sum of two numbers is 9 and the sum of their squares is 261. Find the numbers.
I'm not sure how to set this out algebraically. If you could help me to set it out as a quadratic equation, I should be able to get the answer from there. Thank you for your time.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! The sum of two numbers is 9 and the sum of their squares is 261. Find the numbers.
I'm not sure how to set this out algebraically. If you could help me to set it out as a quadratic equation, I should be able to get the answer from there. Thank you for your time
LET THE NUMBERS BE X AND Y
X+Y=9......................................I
X^2+Y^2=261
USE THE FORMULA
(X+Y)^2+(X-Y)^2=2(X^2+Y^2)
9^2+(X-Y)^2=2*261=522
(X-Y)^2=522-81=441
X-Y=+21..................II...OR....-21..............III
EQN.I+EQN.II
X+Y+X-Y=9+21=30
2X=30
X=15
Y=9-X=9-15=-6
OR
X-Y=-21................................III
EQN.III+EQN.I
2X=-12
X=-6
Y=9-X=9+6=15
HENCE THE 2 NUMBERS ARE 15 AND -6
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