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The sum of two numbers is 12. The sum of the squares of the same two numbers is 90. What are the two numbers?
Natasha35
We get a system of equations:
a+b=12
a2+b2=90.
Replace 12-a for b, and we get:
a2+(12-a)2=90
2a2-24a+144=90
2a2-24a+54=0
a2-12a+27=0
a1=9
a2=3
Because of symmetry, we get two equivalent solutions:
a=9, b=3
or
a=3,b=9
Wiki User
∙ 15y ago
lenpollock
Let the numbers be l & m .
Hence
Sum l + m = 12
Sum of the squares is l^2 + m^2 = 90
Hemce
l = 12 - m
l^2 = ( 12 - m)^2
l^2 = 144 - 24m + m^2
Substitute
144 - 24m + m^2 + m^2 = 90
2m^2 - 24m = -54
m^2 - 12m = -27
m^2 - 12m + 27 = 0
Factor
(m - 3)(m - 9) =0
m = 3 & m = 9 are the two numbers.
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