Question

Question #4bc5b

Answer 1

`{(xle 13/2),(x ge 5/2):}`

Explanation:

We have equivalently

`sqrt((x-5)^2)+sqrt((x-4)^2) = 4-epsilon^2`

Squaring both sides

`(x-5)^2+(x-4)^2+2 sqrt((x-5)^2)sqrt((x-4)^2) =(4-epsilon^2)^2`

but

`2 sqrt((x-5)^2)sqrt((x-4)^2) =(4-epsilon^2)^2-((x-5)^2+(x-4)^2)`

and now squaring again

`4(x-5)^2(x-4)^2 = ((4-epsilon^2)^2-((x-5)^2+(x-4)^2))^2`

now developing and factoring we get at

`(2x-13+epsilon^2)(2x-5-epsilon^2)(epsilon^2-3)(epsilon^2-5)=0`

now we follow with the conditions

`{(2x-13+epsilon^2=0),(2x-5-epsilon^2=0):}`

or

`{(2x=13-epsilon^2=0),(2x =5+epsilon^2=0):}`

and then

`{(xle 13/2),(x ge 5/2):}`