Question

If x = 4 – √15 then x + ¹⁄ₓ =

Answer 1

Solution

Given :-

• x = (4 - √15)

Find :-

• Value of x + 1/x

Explanation

First Calculate, 1/x

==> 1/x = 1/(4 - √15)

Rationalize denominator ,

Multiply by ( 4 + √15) denominator & numerator in right side.

==> 1/x = (4 + √15)/(4-√15)(4+√15)

==> 1/x = (4 + √15)/(4² - √15²)

==> 1/x = (4 + √15)/16 - 15)

==> 1/x = (4 + √15)/1

==>1/x = (4 + √15)

Now, calculate value of x + 1/x

= 1/x + x

Keep value of x & 1/x

= (4 + √15) + (4 - √15)

= 4 + 4 - √15 + √15

= 8

Hence

• Value of ( x + 1/x) will be = 8

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