Bentuk sederhana 418−6632+26\frac{4\sqrt{18}-6\sqrt{6}}{3\sqrt{2}+2\sqrt{6}}32+26418−66 adalah...
(Soal Ujian Nasional 2017)
−24+143-24+14\sqrt{3}−24+143
24+14324+14\sqrt{3}24+143
24−14324-14\sqrt{3}24−143
−24−143-24-14\sqrt{3}−24−143
Alternatif penyelesaian :
418−6632+26×32−2632−26=(418−66)(32−26)18−24\frac{4\sqrt{18}-6\sqrt{6}}{3\sqrt{2}+2\sqrt{6}}\times\frac{3\sqrt{2}-2\sqrt{6}}{3\sqrt{2}-2\sqrt{6}}=\frac{\left(4\sqrt{18}-6\sqrt{6}\right)\left(3\sqrt{2}-2\sqrt{6}\right)}{18-24}32+26418−66×32−2632−26=18−24(418−66)(32−26)
=(418−66)(32−26)−6=\frac{\left(4\sqrt{18}-6\sqrt{6}\right)\left(3\sqrt{2}-2\sqrt{6}\right)}{-6}=−6(418−66)(32−26)
=12×36−818×6−1812+1236−6=\frac{12\times\sqrt{36}-8\sqrt{18\times6}-18\sqrt{12}+12\sqrt{36}}{-6}=−612×36−818×6−1812+1236
=12×36−8×63−18×23+12×6−6=\frac{12\times\sqrt{36}-8\times6\sqrt{3}-18\times2\sqrt{3}+12\times6}{-6}=−612×36−8×63−18×23+12×6
=72−483−363+72−6=\frac{72-48\sqrt{3}-36\sqrt{3}+72}{-6}=−672−483−363+72
=144−843−6=\frac{144-84\sqrt{3}}{-6}=−6144−843
=−24+143=-24+14\sqrt{3}=−24+143