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

M4maths Previous Puzzles

28 May 2012 solve

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

OPtion

1) 2+sqrt(2)
2) 2+sqrt(3)
3) 3+sqrt(5)
4) 3+sqrt(2)
5) 5+sqrt(3)
6) 5+sqrt(2)
7) 4+sqrt(3)
8) 4+sqrt(2)
9) 2+sqrt(5)
10) none of these

Solution

x+(1/x)=4
so x-(1/x)=sqrt[{x+(1/x)}^2 - 4]
=sqrt(12) = 2sqrt(3)
on adding these 2 eq. we get x = 2+sqrt(3)

Correct Option: 2 Best Solution (16)

Suman   12 years AGO

if x+(1/x)=4
x^2+1=4x

x= 2+sqrt(3)and 2-sqrt(3)

Like? Yes (3) | No (2)  

Dr.Dipin Singh   12 years AGO

x+(1/x)=4
x^2-4x+1=0
x= 2+Root 3 , 2-Root3.

Like? Yes (3) | No (2)  

Shiv Kumar   12 years AGO

x^2+1=4x
x^2-4x+1=0
x^2-4x+4=3 ...Adding 3 on both sides
(x-2)^2=3
x-2=SQRT(3)
x=2+SQRT(3)

Like? Yes (4) | No (3)  

Vidya Sagar   12 years AGO

x + 1/x = 4
x^2 +1 = 4x
x^2 - 4x +1 = 0
Using the quadratic formula, if we find the solutions
The values of x are

2 + sqrt(3) or 2 - sqrt(3)

Like? Yes (1) | No (1)  

kiran   12 years AGO

x^2-4x+1=0
the value of x =2+sqrt(3)

Like? Yes (1) | No (1)  

NANDINI   12 years AGO

x^2-4x+1=0
then
x=(2+sqrt(3)

Like? Yes (2) | No (3)  

Gaurav Sikka   12 years AGO

x.x - 4x + 1 = 0
x= 2 + sqrt(3), 2 - sqrt (3)

Like? Yes (2) | No (3)  

GAURAV KUMAR SRIVASTAV   12 years AGO

x + 1/x = 4
x^2 -4x +1 =0
on solving
x=2+sqrt(3)

Like? Yes (2) | No (3)  

Selva Narayanan A J   12 years AGO

x + (1/x) = 4
then, x^2 -4x +1 = 0,
then, by applying quadratic formula,
roots are 2 + or - sqrt(3)

Like? Yes (3) | No (4)  

Browns MN   12 years AGO

Solving using the formula x=-b +/- sqrtb2-4ac
and takin only positive values we get 2+sqrt(3)

Like? Yes (2) | No (3)  

chiru   12 years AGO

by solving the above equation we get 2+sqrt(3) ,2-sqrt(3) as roots

Like? Yes (1) | No (3)  

Manikanta   12 years AGO

by solving, we get the equation
x^2-4x+1=0 ; to find the roots of the equation
we have
roots = -b +- sqrt(b^2-4ac) / 2a

so we get by solving 2+sqrt(3)

Like? Yes (1) | No (3)  

prithviraj sanningannavar   12 years AGO

x+(1/x)=4
x^2-4x+1=0
so x=(-b + sqrt(b^2-4ac))/2a=(4+2sqrt(3))/2=2+sqrt(3)

Like? Yes (1) | No (3)  

sivakumar   12 years AGO

X+(1/X)=4;
X^2-4X+1=0;
SOLVING THAT YOU GET.
X=2+sqrt(3);

Like? Yes (2) | No (4)  

manudixit   12 years AGO

Basic Quad eq
just Cross multiply the the x
apply the quad formula

Like? Yes (1) | No (3)  

shagun garg   12 years AGO

x+1/X=4 => x^2-4x+1=0
x=4+/-(4*4-4*1*1)^0.5
=2+/-3^0.5
or =2+(3)^0.5

Like? Yes (1) | No (3)