Question

If
$(x + \frac{1}{x}) = 6$
Find the value of:
$(x - \frac{1}{x})$
​

Answer 1

$\boxed{\orange{\bf{ANSWER}}}$

GIVEN:

$x \: + \: \frac{1}{x} = 6$

TO FIND:

$ᴠᴀʟᴜᴇ \: ᴏғ \: x - \frac{1}{x}$

SOLUTION:

$x + \frac{1}{x} = 6$

ʙʏ sǫᴜᴀʀɪɴɢ ʙᴏᴛʜ sɪᴅᴇs

➟$(x + \frac{1}{x})^{2} = {6}^{2}$

➟${x}^{2} + \frac{1}{x^{2}} + 2 = 36$

➟${x}^{2} + \frac{1}{x^{2}} = 34$

ʙʏ sᴜʙᴛʀᴀᴄᴛɪɴɢ 2 ғʀᴏᴍ ʙᴏᴛʜ sɪᴅᴇs

➟${x}^{2} + \frac{1}{x^{2} } \: - 2 = 34 - 2$

➟$(x - \frac{1}{x})^{2} = 32$

➟$x - \frac{1}{x} = \sqrt{32}$

➟$x - \frac{1}{x} = 4 \sqrt{2}$

$\tt\large\green{ᴠᴀʟᴜᴇ \: ᴏғ \: x - \frac{1}{x} \: is \: 4 \sqrt{2} }$

$\tt\pink{@ChocolateWingz❤~}$