Pertanyaan

Jika maka 6 dapat dinyatakan dalam psebagai ….

Jika $open parentheses fraction numerator 1 over denominator square root of 3 end fraction minus fraction numerator 1 over denominator square root of 2 end fraction close parentheses equals p$ maka $6$ dapat dinyatakan dalam p sebagai ….

$fraction numerator 6 p over denominator open parentheses square root of 2 plus square root of 3 close parentheses end fraction$
$fraction numerator 6 p over denominator open parentheses square root of 3 minus square root of 2 close parentheses end fraction$

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

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Pembahasan

Ingat kembali merasionalkan bentuk akar : Persamaan (*)di atas dapat dirasionalkan menjadi :

$fraction numerator 1 over denominator square root of 3 end fraction minus fraction numerator 1 over denominator square root of 2 end fraction equals p fraction numerator square root of 2 over denominator square root of 6 end fraction minus fraction numerator square root of 3 over denominator square root of 6 end fraction equals p fraction numerator square root of 2 minus square root of 3 over denominator square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction equals p fraction numerator open parentheses square root of 2 minus square root of 3 close parentheses over denominator 6 end fraction cross times square root of 6 equals p square root of 6 equals p cross times fraction numerator 6 over denominator open parentheses square root of 2 minus square root of 3 close parentheses end fraction square root of 6 equals fraction numerator 6 p over denominator open parentheses square root of 2 minus square root of 3 close parentheses end fraction space space horizontal ellipsis space space left parenthesis asterisk times right parenthesis$

Ingat kembali merasionalkan bentuk akar :

$fraction numerator 1 over denominator square root of a plus square root of b end fraction equals fraction numerator 1 over denominator square root of a plus square root of b end fraction cross times fraction numerator square root of a minus square root of b over denominator square root of a minus square root of b end fraction$

Persamaan (*) di atas dapat dirasionalkan menjadi :

$square root of 6 equals fraction numerator 6 p over denominator open parentheses square root of 2 minus square root of 3 close parentheses end fraction cross times fraction numerator open parentheses square root of 2 plus square root of 3 close parentheses over denominator open parentheses square root of 2 plus square root of 3 close parentheses end fraction equals fraction numerator 6 p open parentheses square root of 2 plus square root of 3 close parentheses over denominator 2 minus 3 end fraction equals negative 6 p open parentheses square root of 2 plus square root of 3 close parentheses$