1. Two positive integers differ by 5. The sum of their squares is 157. Find the numbers.
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1. Two positive integers differ by 5. The sum of their squares is 157. Find the numbers.
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Answer:
6 and 11
Step-by-step explanation:
let x = one number
y = other number
x - y = 5 . ========= x = y + 5
x^2 + y^2 = 157
Substitute y + 5 to x
(y +5)^2 + y^2 = 157
y^2 + 10y + 25 + y^2 = 157
2y^2 + 10y +25 - 157 = 0
2y^2 + 10y - 132 = 0
2 ( y^2 + 5y - 66 ) = 0
2 ( y +11 ) ( y - 6) = 0
y = -11 ; y = 6
y = 6 ( one number)
x - 6 = 5
x = 6 + 5 = 11 ( the other number)