Pertanyaan

Bentuk sederhana dari adalah ....

Bentuk sederhana dari $begin mathsize 14px style fraction numerator open parentheses square root of 3 plus square root of 7 close parentheses open parentheses square root of 3 minus square root of 7 close parentheses over denominator 2 square root of 5 minus 4 square root of 2 end fraction end style$ adalah ....

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

3 + 7 3 - 7 2 5 - 4 2

$begin mathsize 14px style straight i right parenthesis Kalikan space bentuk space pada space pembilang. space Ingat space bahwa space space space open parentheses straight a plus straight b close parentheses open parentheses straight a minus straight b close parentheses equals straight a squared minus straight b squared space space space Sehingga space space space open parentheses square root of straight a plus square root of straight b close parentheses open parentheses square root of straight a minus square root of straight b close parentheses equals straight a minus straight b space space space fraction numerator open parentheses square root of 3 plus square root of 7 close parentheses open parentheses square root of 3 minus square root of 7 close parentheses over denominator 2 square root of 5 minus 4 square root of 2 end fraction equals fraction numerator 3 minus 7 over denominator 2 square root of 5 minus 4 square root of 2 end fraction equals fraction numerator negative 4 over denominator 2 square root of 5 minus 4 square root of 2 end fraction ii right parenthesis Rasionalkan space bentuk space pecahan space tersebut space space space space fraction numerator straight a over denominator square root of straight b minus square root of straight c end fraction equals fraction numerator straight a over denominator square root of straight b minus square root of straight c end fraction. fraction numerator square root of straight b plus square root of straight c over denominator square root of straight b plus square root of straight c end fraction equals fraction numerator straight a open parentheses square root of straight b plus square root of straight c close parentheses over denominator straight b minus straight c end fraction space space space space fraction numerator negative 4 over denominator 2 square root of 5 minus 4 square root of 2 end fraction equals fraction numerator negative 4 over denominator 2 square root of 5 minus 4 square root of 2 end fraction. fraction numerator 2 square root of 5 plus 4 square root of 2 over denominator 2 square root of 5 plus 4 square root of 2 end fraction equals fraction numerator negative 4 open parentheses 2 square root of 5 plus 4 square root of 2 close parentheses over denominator open parentheses 2 square root of 5 close parentheses squared minus open parentheses 4 square root of 2 close parentheses squared end fraction space space space space equals fraction numerator negative 4 open parentheses 2 square root of 5 plus 4 square root of 2 close parentheses over denominator 20 minus 32 end fraction space space space space equals fraction numerator negative 4 open parentheses 2 square root of 5 plus 4 square root of 2 close parentheses over denominator negative 12 end fraction space space space space equals fraction numerator open parentheses 2 square root of 5 plus 4 square root of 2 close parentheses over denominator 3 end fraction equals 2 over 3 open parentheses square root of 5 plus 2 square root of 2 close parentheses end style$