Question

The sum of a number and its reciprocal is one eighth of 34. What is the producto
square root?​

Answer 1

ʟᴇᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ. ʙᴇ x

ɪᴛꜱ ʀᴇᴄɪᴩʀᴏᴄᴀʟ =1/x

ᴀᴛq

x+1/x=1/8×34

x²+1/x=34/8

x²+1=34/8x

8x²+8=34x(ᴍᴜʟᴛɪᴩʟy ʙᴏᴛʜ ꜱɪᴅᴇꜱ ʙy 8)

8x²-34x+8=0

4x²-17x+4=0

ꜱᴏʟᴠɪɴɢ ᴛʜɪꜱ qᴜᴀᴅʀᴀᴛɪᴄ ʙy ꜱᴩʟɪᴛᴛɪɴɢ ᴛʜᴇ ᴍɪᴅᴅʟᴇ ᴛᴇʀᴍ

4x²-16x-x+4=0

4x(x-4)-1(x-4)=0

(4x-1)(x-4)=0

x-4=0_ᴏʀ_ 4x-1=0

x=4____ᴏʀ___x=1/4

ᴩʀᴏᴅᴜᴄᴛ = 4×2=8.

=4×1/2=2

ᴛʜᴀᴛꜱ ᴡʜᴀᴛ ᴡᴇ ᴀʀᴇ ʀᴇqᴜɪʀᴇᴅ

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