Question

if a is equal to root 3 minus root 2 / root 3 + root 2and b is equal to root 3 + root 2 / root 3 minus root 2 find the value of a square + b square + 5 a b

Answer 1

a=√3-√2/√3+√2
b=√3+√2/√3-√2
a²+b²+5ab=(√3-√2/√3+√2)²+(√3+√2/√3-√2)²+5(√3-√2/√3+√2)(√3+√2/√3-√2)
=3+2/3+2+√2+√6-√2-2/√3+√6-2/√3+3+2/3+2+√2-√6+√2-2/√3-√6-2/√3+5(3-2/3-2+√2-√6-√2+2/√3+√6+2/√3)
=10+4/3+2√2+5(1+4/√3)
=30/4+2√2+5+20/√3
=15/2+5+2/√2+20/√3
25/2+2(√2+10√3)