Question

If x=5/4-√11, find x+5/x

Answer 1

X = 5 / 4 - √ 11

Now we should rationalize the denominator..

X = 5(4+√11)/(4-√11)(4+√11)

X= 5(4+√11)/(4^2 - (√11)^2)

X = 5(4+√11)/(16 -11)

X = 5(4+√11)/5

X = 4 + √11

now ,

1/x = 1/ 4+√11

again after rationalising,

1/X = 1(4-√11)/(4+√11)(4-√11)

1/X = 4-√11/5

X + 5/ X= X + 5* 1/X

= 4 + √11 + 5 * (4-√11)/5

= 4+√11 + 4 - √11

= 8