156247

Look at picture 1st

AB = -6+2√2
BC = 2-4√2
CA = 7+7√2

Therefore A²B²C² = (-6+2√2)(2-4√2)(7+7√2)
= 196

Square root both sides

ABC = ± 14

Divide by AB = -6+2√2

C = 3+√2 or -3-√2

Make A the subject of CA = 7+7√2
A =(7+7√2)÷C

Sub C into equation
When C =-3-√2

A =(7+7√2)÷(-3-√2)
=-1-2√2

When C = 3+√2
A =(7+7√2)÷(3+√2)
=1+2√2

Make B the Subject of BC = 2-4√2
B = (2-4√2)÷C

Sub C into the equation
When C =-3-√2
B =(2-4√2)÷(-3-√2)
=-2+2√2

When C =3+√2
B =(2-4√2)÷(3+√2)
=2-2√2

Therefore

A=-1-2√2
B=-2+2√2
C=-3-√2

OR

A= 1+2√2
B= 2-2√2
C= 3+√2