Answer:
Putting the value of x = (5-i√5)÷5 in 5x²-10x+6=0.
We get,
[tex]5(\dfrac{(5-i\sqrt{5})}{5} )^2-10(\dfrac{(5-i\sqrt{5})}{5} ) +6=0\\\\\dfrac{(5-i\sqrt{5})}{5} ^2-2(5-i\sqrt{5} ) +6=0\\\\(5-i\sqrt{5}) ^2-10(5-i\sqrt{5} ) +30=0[/tex]
⇒ 25 + (i√5)² - 10i√5 - 50 + 10i√5 + 30 = 0
⇒ (i√5)² + 5 = 0 {∵ i² = -1}
⇒ - 5 + 5 = 0
⇒ 0 = 0
Thus, (5-i√5) ÷ 5 is the solution of 5x²-10x+6=0.
