1.

4. Find two consecutive positive integers, sum of whose squares is 365.​

Answer»

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ʟᴇᴛ ᴛʜᴇ ᴛᴡᴏ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ᴘᴏsɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀs ʙᴇ x ᴀɴᴅ x+1

ᴛʜᴇɴ,

x

2

+(x+1)

2

=365

⇒x

2

+x

2

+2x+1=365

⇒2x

2

+2x−364=0

⇒x

2

+x−182=0

ᴜsɪɴɢ ᴛʜᴇ ǫᴜᴀᴅʀᴀᴛɪᴄ ғᴏʀᴍᴜʟᴀ, ᴡᴇ ɢᴇᴛ

x=

2

−1±

1+728

⇒

2

−1±27

  • ⇒x=13 ᴀɴᴅ x=−14

ʙᴜᴛ x ɪs ɢɪᴠᴇɴ ᴛᴏ ʙᴇ ᴀ ᴘᴏsɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀ. ∴x

  • =−14

ʜᴇɴᴄᴇ, ᴛʜᴇ ᴛᴡᴏ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ᴘᴏsɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀs ᴀʀᴇ 13 ᴀɴᴅ 14.


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