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
