Question

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

Answer 1

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

We get,

`5(((5-i√(5)))/(5) )^2-10(((5-i√(5)))/(5) ) +6=0\\\\((5-i√(5)))/(5) ^2-2(5-i√(5) ) +6=0\\\\(5-i√(5)) ^2-10(5-i√(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.