Question

If x=4-√17 find 1 /x

Answer 1

Answer:

$\huge\boxed{\sf -4-\sqrt{17}}$

Step-by-step explanation:

$\displaystyle \frac{1}{x} = \frac{1}{4-\sqrt{17} }\\\\Multiplying \ and \ dividing \ by \ conjugate \ 4 + \sqrt{17} \\\\= \frac{1}{4-\sqrt{17} } \times \frac{4+\sqrt{17} }{4+\sqrt{17} } \\\\= \frac{4 + \sqrt{17} }{(4)^2-(\sqrt{17} )^2} \ \ \ by \ formula \ (a+b)(a-b)=a^2-b^2\\\\= \frac{4+\sqrt{17} }{16 - 17} \\\\= \frac{4+\sqrt{17} }{-1} \\\\= -(4+\sqrt{17} )\\\\= -4-\sqrt{17} \\\\\rule[225]{225}{2}$

Hope this helped!

~AH1807

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Answer 2

Step-by-step explanation:

Given that:

x = 4-√17

Therefore, 1/x = 1/(4-√17)

Now, the denominator is 4-√17

We know that

Rationalising factor of a-√bc is a+√bc.

Therefore, the rationalising factor of 4-√17 is 4+√17.

On rationalising the denominator them

⇛[1/(4-√17)]×[(4+√17)/4+√17)]

⇛[1(4+√17)]/[(4-√17)(4+√17)]

Since, (a-b)(a+b) = a²-b²

Where,

• a = 4 and
• b = √17

⇛[1(4+√17)]/[(4)²-(√17)²]

⇛[1(4+√17)]/(4*4)-√(17*17)]

⇛[4+√17]/[16 - 17]

⇛(4+√17)/1

⇛1/x = 4+√17 ans.

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