Question

Solve 2(x+1/x)^2-7(x+1/x)+5=0
If you answer it correctly then I will mark you as Brainerd
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Answer 1

Answer:

answer of this is x= 2/3

Step-by-step explanation:

explaned in uploaded image.

Answer 2

Answer:

x = 2 , 1/2

Solution:

Here,

The given equation is ;

2(x + 1/x)² - 7(x + 1/x) + 5 = 0

Putting x + 1/x = y , the above equation will be reduced to ;

=> 2y² - 7y + 5 = 0

=> 2y² - 2y - 5y + 5 = 0

=> 2y(y - 1) - 5(y - 1) = 0

=> (y - 1)(2y - 5) = 0

=> y = 1 , 5/2

Case (1) : If y = 1

=> y = 1

=> x + 1/x = 1

=> (x² + 1)/x = 1

=> x² + 1 = x

=> x² - x + 1 = 0

Here,

a = 1 , b = -1 , c = 1

Discriminant , D = b² - 4ac

=> D = (-1)² - 4•1•1

=> D = 1 - 4

=> D = -3

=> D < 0

Since , the discriminant is less than zero , thus , there exist no real roots.

Case (2) : If y = 5/2

=> y = 5/2

=> x + 1/x = 5/2

=> (x² + 1)/x = 5/2

=> 2(x² + 1) = 5x

=> 2x² + 2 = 5x

=> 2x² - 5x + 2 = 0

=> 2x² - 4x - x + 2 = 0

=> 2x(x - 2) - (x - 2) = 0

=> (x - 2)(2x - 1) = 0

=> x = 2 , 1/2

Here,

We got two real roots , x = 2 , 1/2 .

Hence,

The required answer is :

x = 2 , 1/2