Question

√11+4√6+√11-4√6
radical din 11.4radicaldin6 este totul sub radical

Answer 1

formula radicalilor  compusi
√(11+4√6)=√(11+√96)=
=√[11+√(121-96)]/2+√[11-√(121-96)]/2=
=√(11+√25)/2+√(11-√25)]/2=
=√(11+5)/2+√(11-5)]/2=
=√16/2+√6/2=
=√8+√3=
=2√2+√3


√(11-4√6)=√(11-√96)=
=√[11+√(121-96)]/2-√[11-√(121-96)]/2=
=√(11+√25)/2-√(11-√25)]/2=
=√(11+5)/2-√(11-5)]/2=
=√16/2-√6/2=
=√8-√3=
=2√2-√3


√(11+4√6)+√(11-4√6)=2√2+√3+2√2-√3=4√2