Question

the roots of the quadratic equation x+1/x=3​

Answer 1

Topic : Quadratic Equation

Given : x + 1/x = 3

To Find : Roots of the given equation.

Solution :

x + 1/x = 3

Taking LCM and solving,

( x² + 1 ) / x = 3

Cross Multiply,

x² + 1 = 3x

Rearrange,

x² - 3x + 1 = 0

Now, use Quadratic Formula

Quadratic Formula,

Roots of equation ax² + bx + c = 0 can be obtained by using,

x = { -b ± √(b² - 4ac) } / 2a

On comparing ax² + bx + c = 0 with obtained equation, we get

• a = 1
• b = -3
• c = 1

Applying Formula,

x = { -(-3) ± √((-3)² - 4(1)(1) } / 2(1)

x = { 3 ± √( 9 - 4 ) } / 2

x = { 3 ± √5 } / 2

So, two roots of given Quadratic equation are

• ( 3 + √5 ) / 2

• ( 3 - √5 ) / 2