Let us say, the two consecutive positive integers be *x* and *x* + 1.

Therefore, as per the given questions,

*x*^{2} + (*x* + 1)^{2} = 365

⇒ *x*^{2 }+ *x*^{2 }+ 1 + 2*x* = 365

⇒ 2*x*^{2} + 2x – 364 = 0

⇒ *x*^{2 }+ *x *– 182 = 0

⇒ *x*^{2 }+ 14*x* – 13*x* – 182 = 0

⇒ *x*(*x* + 14) -13(*x* + 14) = 0

⇒ (*x* + 14)(*x* – 13) = 0

Thus, either, *x* + 14 = 0 or *x* – 13 = 0,

⇒ *x* = – 14 or *x* = 13

since, the integers are positive, so *x* can be 13, only.

*x* + 1 = 13 + 1 = 14

Therefore, two consecutive positive integers will be 13 and 14.

Answered by Pragya Singh | 1 year agoA natural number when increased by 12 equals 160 times its reciprocal. Find the number.

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is \( \dfrac{29}{20}\) Find the original fraction.

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

The sum of the squares of two consecutive multiple of 7 is 637. Find the multiples.