Question

If x=5-√3/5+√3 and y=5+√3/5-√3, show that x-y =-10√3/ 11

Answer 1

Question

If x=(5-√3)/(5+√3 )and y=(5+√3)/(5-√3) show that x-y = -10√3/ 11

Solution

Given :-

• Value of x = (5-√3)/(5+√3 )
• Value of y = (5+√3)/(5-√3 )

Show That:-

• x-y = -10√3/ 11

Explanation

First rationalize Denominator of x

==> x = (5-√3)(5-√3)/(5+√3 )(5-√3)

==>x = (25 + 3 - 2 * 5 * √3)/(5²-√3²)

==>x = (28 - 10√3)/(25-3)

==> x = (28-10√3)/22

Now, rationalize Denominator of y

==>y = (5+√3)(5+√3)/(5-√3 )(5+√3)

==>y = (25 + 3 + 2 * 5 * √3)/(5²-√3²)

==>y = (28 + 10√3)/(25-3)

==>y = (28 + 10√3)/22

Now, calculate (x - y)

==> x - y

keep New value of x & y

==> [ (28-10√3)/22 ] - [ (28 + 10√3)/22 ]

==> [ 28 - 10√3 - 28 - 10√3]/22

==> -20√3/22

==> -10√3/11

That's proved .

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