1st step: Rationalize the denominator
(√3 + √2) x (√3 + √2)+ √3 - √2/√3 + √2 =p+q√6
Rationalizing
(√3 + √2) x (√3 + √2)+ (√3 - √2)x(√3 - √2 )= p+q√6
2nd step: Write the repeated multiplication in exponential form
(√3 + √2)^2 + (√3 - √2)^2 = p+q√6
3rd step: Expand the expression using (a+b)^2=a^2+2ab+b^2
3+2 √6+2+(√3-√2)^2=p+q√6
3+2 √6+2+3-2√6+2=p+q√6
4th step: Remove "+2 √6" and "-2√6" because they're opposites and add up to zero
3+2+3+2= p+q√6
10= p+q√6
5th step: move p to the other side abs change the sign
-p+10= q√6
-p= q√6 -10
6th step: Change signs on both sides of the equation
p= -q√6 +10
7th step: Write p in parametric form
p= -q√6 +10, q ∈ ℝ
Final answer: p= -q√6 +10, q ∈ ℝ
