Show that 3+2√5 is an irrational number.
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ᎪΝՏᏔᎬᎡ -
Pʀᴏᴠᴇ 3+25 ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ.
→ ʟᴇᴛ ᴛᴀᴋᴇ ᴛʜᴀᴛ 3+25 ɪs ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ
→ sᴏ, ᴡᴇ ᴄᴀɴ ᴡʀɪᴛᴇ ᴛʜɪs ᴀɴsᴡᴇʀ ᴀs
⇒3+25=ʙᴀ
Hᴇʀᴇ ᴀ & ʙ ᴜsᴇ ᴛᴡᴏ ᴄᴏᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀ ᴀɴᴅ ʙ=0.
⇒25=ʙᴀ−3
⇒25=ʙᴀ−3ʙ
∴5=2ʙᴀ−3ʙ
Hᴇʀᴇ ᴀ ᴀɴᴅ ʙ ᴀʀᴇ ɪɴᴛᴇɢᴇʀ sᴏ 2ʙᴀ−3ʙ ɪs ᴀ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ sᴏ 5 sʜᴏᴜʟᴅ ʙᴇ ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ ʙᴜᴛ
5 ɪs ᴀ ɪʀʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ sᴏ ɪᴛ ɪs ᴄᴏɴᴛʀᴀᴅɪᴄᴛ
- Hᴇɴᴄᴇ 3+25 ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ.
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