Question

If x+1/x=17/4


then find the value of x.​

Answer 1

Given that,

$x+\dfrac{1}{x}=\dfrac{17}{4}$

To find,

The value of x.

Solution,

To find the value of x, firstly we need to simplify the given equation.

$\dfrac{x^2+1}{x}=\dfrac{17}{4}$

Now cross multiplying we get:

$4x^2+4=17x\\\\4x^2-17x+4=0$

Now solving the above equation using middle term splitting.

$4x^2-16x-x+4=0\\\\4x(x-4)-1(x-4)=0\\\\(4x-1)(x-4)=0$

So,

$x=\dfrac{1}{4},4$

So, the value of x are 1/4 and 4.

Answer 2

Given :  x   +   1/x    = 17/4

To find : Value of x

Solution:

x   +   1/x    = 17/4

multiplying both sides by 4x

=> 4x²  + 4  = 17x

=> 4x² - 17x  + 4 = 0

=> 4x² - 16x  -x  + 4 = 0

=>  4x(x - 4) - 1(x - 4) = 0

=> (4x - 1) (x - 4) = 0

=> x = 1/4   , x  = 4

=>  1/x = 4  &  1/x = 1/4

Verification :    x + 1/x   = 1/4 + 4  =  4 + 1/4  =  17/4

x =  4  ,  1/4

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