SOLUTION: one positive number is six more than another. the sum of their squares is 260. what are the numbers?
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Question 981315: one positive number is six more than another. the sum of their squares is 260. what are the numbers?
Found 2 solutions by Boreal, ankor@dixie-net.com:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x, x+6 are the numbers
x^2+x^2+12x+36=260
2x^2+12x+36=260
2x^2+12x-224=0
x^2+6x-112=0
(x-8 ) ( x+14 )=0
the positive root is 8
the integers are 8 and 14
the square of 8 is 64
the square of 14 is 196
They add to 260
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
one positive number is six more than another.
x, (x+6) are the number
the sum of their squares is 260.
x^2 + (x+6)^2 = 260
FOIL(x+6)(x+6)
x^2 + x^2 + 6x + 6x + 36 = 260
Combine like terms
2x^2 + 12x + 36 - 260 = 0
2x^2 + 12x - 224 = 0
simplify, divide by 2
x^2 + 6x - 112 = 0
Factors to
(x+14)(x-8) = 0
what are the numbers?
the positive solution
x = 8, and 14 obviously
:
:
See if that works
8^2 + 14^2 =
64 + 196 = 260
:
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