Question

Evaluate 5x^2 − 10x when the value of x is (2-√5)/2

Answer 1

`(5)/(4)`

Explanation:

To evaluate :

5x² − 10x

value of x =
`(2-\sqrt5)/(2)`

Now,

substituting the value of x in the given equation, we get

⇒
`5((2-\sqrt5)/(2))^2-10((2-\sqrt5)/(2))`

or

⇒
`5(((2-\sqrt5)^2)/(4))-5(2-\sqrt5)`

taking 2 - √5 as common, we get

⇒ (2 - √5)
`((5(2-\sqrt5))/(4))-5)`

or

⇒ (2 - √5)
`((10-5\sqrt5))/(4))-5`

or

⇒ (2 - √5)
`*((10-5\sqrt5-4*5)/(4))`

or

⇒ (2 - √5)
`*((10-5\sqrt5-20)/(4))`

or

⇒ (2 - √5)
`*((-10-5\sqrt5)/(4))`

or

⇒
`2*((-10-5\sqrt5)/(4))-\sqrt5*((-10-5\sqrt5)/(4))`

or

⇒
`((-10-5\sqrt5)/(2))-((-10*\sqrt5-5*5)/(4))`

or

⇒
`((-10-5\sqrt5)/(2))-((-10*\sqrt5-25)/(4))`

or

⇒
`(4*(-10-5\sqrt5)-(2*(-10*\sqrt5-25))/(2*4)`

or

⇒
`((-40-20\sqrt5)-(-20*\sqrt5-50))/(8)`

or

⇒
`((-40-20\sqrt5)+20*\sqrt5+50))/(8)`

or

⇒
`(10)/(8)`

or

⇒
`(5)/(4)`