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given,

(a)²+(a+1)²= 365

a²+a²+2a+1 = 365

⇒2a²+2a+1 = 365

⇒2a²+2a-364= 0

⇒a²+a-182 = 0

⇒(a-13)x(a+14) = 0

⇒a = 13,-14

as they said positive integers

a=-14 is not possible

⇒a = 13

the two consecutive positive integers are 13,14

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So the two numbers be x , x+1

so given

x² + (x+1)² = 365

x² + x² + 1 + 2x = 365

2x² + 2x - 364 = 0

x² + x - 182 = 0

x² + 14x - 13x - 182 = 0

x(x + 14) - 13(x + 14) = 0

(x - 13)(x + 14) = 0

so x = 13

so the

consequetive numbers are 13,14

so given

x² + (x+1)² = 365

x² + x² + 1 + 2x = 365

2x² + 2x - 364 = 0

x² + x - 182 = 0

x² + 14x - 13x - 182 = 0

x(x + 14) - 13(x + 14) = 0

(x - 13)(x + 14) = 0

so x = 13

so the

consequetive numbers are 13,14