Math, asked by anandurkurup101, 1 year ago

Find two consecutive positive integers, the sum of whose squares is 365

Answers

Answered by Muthu2004
2

Answer: 13, 14


Step-by-step explanation:


After the following steps, the answer is


Neglecting the negative value


x=13


The two consecutive no is x=13, x+1 =13+1 =14

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anandurkurup101: THAnks bro
Muthu2004: I am sis. Mark as brainliest
Answered by Anonymous
2

sᴏʟᴜᴛɪᴏɴ:

  ʟᴇᴛ ᴛʜᴇ ᴛᴡᴏ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ɴᴜᴍʙᴇʀs ʙᴇ x ᴀɴᴅ x+1.

   ᴛʜᴇʀᴇғᴏʀᴇ ,

  x² + (x+1)² = 365      x² + x² +1² + 2*x*1 = 365 (ʙᴇᴄᴀᴜsᴇ (ᴀ+ʙ)² = ᴀ² + ʙ²+ 2ᴀʙ)

       ᴏʀ 2x² + 1 + 2x = 365

         2x² + 2x = 365 - 1

         2x² + 2x = 364

         2(x² + x) = 364

       ᴏʀ x² + x = 364/2

       ᴏʀ x² + x = 182

     ᴏʀ x² + x - 182 =0

     ɴᴏᴡ sᴏʟᴠᴇ ᴛʜᴇ ϙᴜᴀᴅʀᴀᴛɪᴄ ᴇϙᴜᴀᴛɪᴏɴ ,

       x² + 14x - 13x - 182 = 0

   ɴᴏᴛᴇ : - 13 *14 = 182 , ᴛʜɪs ɪs ʙᴇᴄᴀᴜsᴇ ɪ ᴡʀɪᴛᴇ 14x - 13x ɪɴsᴛᴇᴀᴅ ᴏғ x , sᴏ ᴀs ᴛᴏ sᴏʟᴠᴇ ᴛʜᴇ ϙᴜᴀᴅʀᴀᴛɪᴄ ᴇϙᴜᴀᴛɪᴏɴ .

           x (x+14) - 13 (x +14 ) = 0

          ( x- 13 )(x+14)=0

  ᴛʜᴇʀᴇғᴏʀᴇ , ᴇɪᴛʜᴇʀ x - 13 = 0 ᴏʀ x+14 =0

  sɪɴᴄᴇ ᴛʜᴇ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀs ᴀʀᴇ ᴘᴏsɪᴛɪᴠᴇ ,

    ᴛʜᴇʀᴇғᴏʀᴇ , x-13 = 0

             ⇒ x =13

ʜᴇɴᴄᴇ ᴏɴᴇ ᴏғ ᴛʜᴇ ᴘᴏsɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀs = 13 ,

ᴛʜᴇʀᴇғᴏʀᴇ ᴏᴛʜᴇʀ ᴘᴏsɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀ = x+1 = 13+1 = 14

sᴏ ᴛʜᴇ ᴛᴡᴏ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ᴘᴏsɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀs ᴀʀᴇ 13 ᴀɴᴅ 14 .

ʜᴏᴘᴇ ᴛʜɪs ʜᴇʟᴘs ʏᴏᴜ !!

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