Question

已知:a=1/√3+2,b=1/√3-2,求√3a^2+4ab+3b^2

Answer 1

a=1/(√3 + 2)=2 - √3 ,b = 1/(√3 -2)= -2 - √3,

则,a+b=-2√3 ,ab=-1

√(3a^2+4ab+3b^2)

=√[3(a²+b²)+4ab]

=√[3(a+b)²-2ab]

=√(3×12+2)

=√38