Question

If x= 3+root7/2,then find the value of 4x ​2 +1/x 2.

Answer 1

4×2(3+√7÷2)+½(3+√7÷2)
=8×3+8√7÷2+3÷2+√7÷4
=24+1.5+4√7+√7÷4
=(96+6+16√7+√7)÷4
=(102+17√7)÷4
=25.5+3.75√7
=35.42

Answer 2

Answer:

32

Step-by-step explanation:

$4x^2 +\frac{1}{x^2}$   = $(2x+ \frac{1}{x} )^2 -4$  ......... (1)

Now,2x = 2($\frac{3 +\sqrt{7} }{2}$) =3+√7,  $\frac{1}{x}$ =$\frac{1}{\frac{3+\sqrt{7} }{2} } =\frac{2}{3+\sqrt{7} } =\frac{2(3-\sqrt{7}) }{(3+\sqrt{7} )(3-\sqrt{7} )} = \frac{2(3-\sqrt{7}) }{9-7 } =\frac{2(3-\sqrt{7}) }{2 } =3-\sqrt{7}$

Now in (1) we put x=3+√7 and  $\frac{1}{x}$ =3-√7

$4x^2 +\frac{1}{x^2}$   = $(2x+ \frac{1}{x} )^2 -4$ = {(3+√7 ) +(3-√7 )}²  -4

= (6)² -4=36-4 =32