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

Answer:[tex]\frac{5}{4}[/tex]Step-by-step explanation:To evaluate :5x² − 10xvalue of x = [tex]\frac{2-\sqrt5}{2}[/tex]Now,substituting the value of x in the given equation, we get⇒ [tex]5(\frac{2-\sqrt5}{2})^2-10(\frac{2-\sqrt5}{2})[/tex]or⇒ [tex]5(\frac{(2-\sqrt5)^2}{4})-5(2-\sqrt5)[/tex]taking 2 - √5 as common, we get⇒ (2 - √5)[tex](\frac{5(2-\sqrt5)}{4})-5)[/tex]or⇒ (2 - √5)[tex](\frac{10-5\sqrt5)}{4})-5[/tex]or⇒ (2 - √5)[tex]\times(\frac{10-5\sqrt5-4\times5}{4})[/tex]or⇒ (2 - √5)[tex]\times(\frac{10-5\sqrt5-20}{4})[/tex]or⇒ (2 - √5)[tex]\times(\frac{-10-5\sqrt5}{4})[/tex]or⇒ [tex]2\times(\frac{-10-5\sqrt5}{4})-\sqrt5\times(\frac{-10-5\sqrt5}{4})[/tex]or⇒ [tex](\frac{-10-5\sqrt5}{2})-(\frac{-10\times\sqrt5-5\times5}{4})[/tex]or⇒ [tex](\frac{-10-5\sqrt5}{2})-(\frac{-10\times\sqrt5-25}{4})[/tex]or⇒ [tex]\frac{4\times(-10-5\sqrt5)-(2\times(-10\times\sqrt5-25)}{2\times4}[/tex]or⇒ [tex]\frac{(-40-20\sqrt5)-(-20\times\sqrt5-50)}{8}[/tex]or⇒ [tex]\frac{(-40-20\sqrt5)+20\times\sqrt5+50)}{8}[/tex]or⇒ [tex]\frac{10}{8}[/tex]or⇒ [tex]\frac{5}{4}[/tex]