Question

If a=√3-√2 ÷√3+√2 and b=√3+√2÷√3-√2 then find a^2+b^2+2ab

Answer 1

Rationalize RHS of both a and b

a=(3√+2√)(3√+2√)(3√+2√)(3√−2√)a=(3+2)(3+2)(3+2)(3−2)

a=(3–√+2–√)2a=(3+2)2

a=5+26–√a=5+26

Similary

b=5−26–√b=5−26

a2+b2=(a+b)2−2aba2+b2=(a+b)2−2ab
Then question become a^2+b^2+2ab-2ab

=(5+26–√+5−26–√)2−2(5+26–√)(5−26–√)=(5+26+5−26)2−2(5+26)(5−26)

=100−2(25−24)=100−2(25−24)

=98=98