SOLUTION: the sum of 2 numbers is 18. the sum of their squares is 4 more than 16 times the larger number. find the numbers

Question 660875: the sum of 2 numbers is 18. the sum of their squares is 4 more than 16 times the larger number. find the numbers
Answer by ReadingBoosters(3246) (Show Source): You can put this solution on YOUR website!
x + y = 18
x^2 + y^2 = 4 + 16x
Substitute x = 18 - y into the second equation
(18 - y)^2 + y^2 = 4 + 16(18-y)
(18-y)(18-y) + y^2 = 4 + 288 - 16y
324 - 18y - 18y + y^2 + y^2 = 292 - 16y
324 - 36y + 2y^2 = 292 - 16y
32 - 20y + 2y^2 = 0
Rearrange
2y^2 - 20y + 32
2(y^2 - 10y + 16)
2(y - )(y - ) both minus as the - 10y and + 16
multiples of 16: 16,1; 4,4; 8,2
choosing 8,2 as they add up to 10
2(y-8)(y-2)=0
(y-8)(y-2)=0*2
y=8
y=2
x=18-8 = 10
x=18-2 = 16
Could be 8 and 10
Could also be 2 and 16
Proof
8+10 = 18; 8^2 + 10^2 = 164
16*10 = 160 + 4= 164
2+16 = 18; 2^2 + 16^2 = 260
16*16 = 256 + 4 = 260
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