Question

What is the solution set of the following equation?

4/5x^2=2x-4/5

1. {1, 2}
2. {1, 1/2}
3. {2, 1\2}

Answer 1

{2, 1\2}

Step-by-step explanation:

Answer 2

multiply both sides by 5
4x^2=10x-4
divide both sides by 2
2x^2=5x-2
minus 5x from both sides and add 2 to both sides
2x^2-5x+2=0
use quadratic formula
for
ax^2+bx+c=0
x=
`(-b+/- √(b^2-4ac) )/(2a)`

given
2x^2-5x+2=0
a=2
b=-5
c=2
x=
`(-(-5)+/- √((-5)^2-4(2)(2)) )/(2(2))`
x=
`(5+/- √(25-16) )/(4)`
x=
`(5+/- √(9) )/(4)`
x=
`(5+/- 3)/(4)`
x=(5+3)/4 or (5-3)/4
x=8/4 or 2/4
x=2 or 1/2

3rd option is correct