Question

If x is equal to 4 minus root 15 find the value of x plus one by x whole power 2

Answer 1

Given :

$x = 4 - \sqrt{15}$

To find :

$(x + 1 \div x) {}^{2}$

Let us first find out 1/x

1/x = 1 / 4 –√15

= ( 1 / 4 – √15 ) × [ ( 4+ √15 ) / ( 4 + √15 ) ]

= [ ( 4 + √15 ) / ( 16 – 15 ) ]

= 4 + √15

Now,

( x + 1/x )² = [ 4 – √15 + 4 + √15 ]²

= [ 8 ]²

= 64

Hope the solution is clear to you!!

All the best.