sum means +
positive number = x
x^2 + (x+4)^2 = 170
[tex] {x}^{2} + {(x + 4)}^{2} = 170 \\ {x}^{2} + {x}^{2} + 8x + 16 = 170 \\ 2 {x}^{2} + 8x = 154 \: - - > \div 2 \\ {x}^{2} + 4x = 77 [/tex]
[tex]{x}^{2} + 4x - 77 = 0 \\ (x - 7)(x + 11) = 0 \\ x = 7 \: or \: - 11[/tex]
since it says the number (x) is a POSITIVE, then it can only be x = 7
**you can also plug it into:
[tex] {x}^{2} + {(x + 4)}^{2} = 170 \\ {7}^{2} + {(7 + 4)}^{2} = 170 \\ 49 + {(11)}^{2} = 49 + 121 = 170 \\ ✔[/tex]
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