Question

Show by substitution that(5-i√5)/5 is a solution to 5x²-10x+6=0.

Answer 1

Answer:

Putting the value of x = (5-i√5)÷5 in 5x²-10x+6=0.

We get,

$5(\dfrac{(5-i\sqrt{5})}{5} )^2-10(\dfrac{(5-i\sqrt{5})}{5} ) +6=0\\\\\dfrac{(5-i\sqrt{5})}{5} ^2-2(5-i\sqrt{5} ) +6=0\\\\(5-i\sqrt{5}) ^2-10(5-i\sqrt{5} ) +30=0$

⇒ 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.