Question

if x+squareroot(15)=4 then x+1/x=?

Answer 1

hlo mate
here is ur answer in the attachment

Answer 2

Answer:

Numeric value of x + 1 / x is 8 .

Step-by-step explanation:

It is given that the x + √15 is equal to 4.

= >  x + √15 = 4

= >  x = 4 - √15      ...( i )

Now, reciprocal the value of x,

= >  1 / x = 1 / ( 4 - √15 )

By Rationalization, multiply and divide by ( 4 + √15 ) on right hand side.

$\implies\dfrac{1}{x} =\dfrac{1}{4-\sqrt{15}}\times\dfrac{4+\sqrt{15}}{4+\sqrt{15}}$

From the identities of factorization, we know the value of ( a + b )( a - b ) remains a^2 - b^2.

So, ( 4 + √15 )( 4 - √15 ) =  4^2 - ( √15 )^2 = 16 - 15 = 1

= >  1 / x = ( 4 + √15 ) / 1

= >  1 / x = 4 + √15   ...( ii )

Now, add ( i ) and ( ii ) ,

= >  x + 1 / x = 4 - √15 + 4 + √15

= >  x + 1 / x = 4 + 4

= >  x + 1 / x = 8