in δabc (m∠c = 90°), the points d and e are the points where the angle bisectors of ∠a and ∠b intersect respectively sides
bc
and
ac
. point g ∈
ab
so that
dg
⊥
ab
and h ∈
ab
so that
eh
⊥
ab
.

find ec

its 50 miles away from the starting point

step-by-step explanation:

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0