Question

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Find two consecutive positive integer sum of whose squares is 365..!!​

Answer 1

Answer:

182,183

Explanation:

Suppose these 2 no. are x and x+1

so x+x+1 equals 365

through this equation the answer will come

Answer 2

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Let the two consecutive positive integers be x and x + 1

Then,

x2 +(x+1) 2 =365

⇒x2 +x2 + 2x + 1 = 365

⇒2 x2 +2x − 364 = 0

⇒x2 + x − 182 = 0

Using the quadratic formula, we get

x= 2 −1 ± 1 + 728

⇒2 − 1 ± 27

⇒x = 13 and x = −14

But x is given to be a positive integer.

∴x1 = −14

Hence, the two consecutive positive integers are 13 and 14.