Question

(3-√2) * (5+√8)= (4-√3) * (√3+6)= Упростите выражение

Answer 1

$(3- \sqrt{2} ) * (5+ \sqrt{8} )=11+ \sqrt{2 } \\ \\ (3- \sqrt{2} ) * (5+ \sqrt{8} )=3*5-\sqrt{2}*5+3 \sqrt{8}- \sqrt{2} * \sqrt{8} = \\ =15-5\sqrt{2}+3\sqrt{4*2}- \sqrt{2*8} =15-5 \sqrt{2} +3\sqrt{2^2*2}- \sqrt{16} = \\ =15-5 \sqrt{2} +3*2\sqrt{2}- \sqrt{4^2} =15-5 \sqrt{2} +6\sqrt{2}- 4 = \\ =11+ \sqrt{2 }$



$(4- \sqrt{3} ) * ( \sqrt{3} +6)=21-2 \sqrt{3} \\ \\ (4- \sqrt{3} ) * ( \sqrt{3} +6)=4 \sqrt{3} - \sqrt{3} * \sqrt{3} +4*6- \sqrt{3} *6= \\ =4 \sqrt{3} -3+24-6 \sqrt{3} =21-2 \sqrt{3}$