Pertanyaan

Sederhanakanlah 2 + 1 2 + 3 + 2 2 + 3 2 2 + 1 + 2 − 1 2 + 1 .

Sederhanakanlah $\frac{2 + 3}{2 + 1} + \frac{2 2 + 1}{2 2 + 3} + \frac{2 + 1}{2 - 1}$ .

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Habis dalam

Klaim

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

bentuk sederhana dari .

bentuk sederhana dari $fraction numerator square root of 2 plus 3 over denominator square root of 2 plus 1 end fraction plus fraction numerator 2 square root of 2 plus 1 over denominator 2 square root of 2 plus 3 end fraction plus fraction numerator square root of 2 plus 1 over denominator square root of 2 minus 1 end fraction$ .

Pembahasan

Ingat bahwa: Menyederhanakan bentuk akar: Jadi, bentuk sederhana dari .

Ingat bahwa:

$a over c plus-or-minus b over c equals fraction numerator a plus-or-minus b over denominator c end fraction$
$fraction numerator a over denominator square root of b plus square root of c end fraction equals fraction numerator a over denominator square root of b plus square root of c end fraction times fraction numerator square root of b minus square root of c over denominator square root of b minus square root of c end fraction equals fraction numerator a open parentheses square root of b plus square root of c close parentheses over denominator b minus c end fraction$

Menyederhanakan bentuk akar:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 plus 3 over denominator square root of 2 plus 1 end fraction plus fraction numerator 2 square root of 2 plus 1 over denominator 2 square root of 2 plus 3 end fraction plus fraction numerator square root of 2 plus 1 over denominator square root of 2 minus 1 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 2 plus 3 close parentheses open parentheses 1 plus square root of 2 close parentheses over denominator open parentheses 1 plus square root of 2 close parentheses open parentheses square root of 2 minus 1 close parentheses open parentheses 2 square root of 2 plus 3 close parentheses end fraction plus fraction numerator 2 square root of 2 plus 1 over denominator open parentheses 1 plus square root of 2 close parentheses open parentheses square root of 2 minus 1 close parentheses open parentheses 2 square root of 2 plus 3 close parentheses end fraction end cell row blank blank cell plus fraction numerator open parentheses square root of 2 plus 1 close parentheses open parentheses 5 square root of 2 plus 7 close parentheses over denominator open parentheses 1 plus square root of 2 close parentheses open parentheses square root of 2 minus 1 close parentheses open parentheses 2 square root of 2 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses square root of 2 plus 3 close parentheses open parentheses 1 plus square root of 2 close parentheses plus 2 square root of 2 plus 1 plus open parentheses square root of 2 plus 1 close parentheses open parentheses 5 square root of 2 plus 7 close parentheses over denominator open parentheses 1 plus square root of 2 close parentheses open parentheses square root of 2 minus 1 close parentheses open parentheses 2 square root of 2 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 3 plus square root of 2 close parentheses open parentheses 1 plus square root of 2 close parentheses plus 2 square root of 2 plus 1 plus open parentheses 1 plus square root of 2 close parentheses open parentheses 5 square root of 2 plus 7 close parentheses over denominator 1 times open parentheses 2 square root of 2 plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses 3 plus square root of 2 close parentheses open parentheses 1 plus square root of 2 close parentheses plus 2 square root of 2 plus 1 plus open parentheses 1 plus square root of 2 close parentheses open parentheses 5 square root of 2 plus 7 close parentheses over denominator 2 square root of 2 plus 3 end fraction end cell row blank equals cell fraction numerator 4 square root of 2 plus 5 plus 2 square root of 2 plus 1 plus open parentheses square root of 2 plus 1 close parentheses open parentheses 5 square root of 2 plus 7 close parentheses over denominator 2 square root of 2 plus 3 end fraction end cell row blank equals cell fraction numerator 4 square root of 2 plus 5 plus 2 square root of 2 plus 1 plus 17 plus 12 square root of 2 over denominator 2 square root of 2 plus 3 end fraction end cell row blank equals cell fraction numerator 18 square root of 2 plus 23 over denominator 2 square root of 2 plus 3 end fraction end cell row blank equals cell fraction numerator open parentheses 18 square root of 2 plus 23 close parentheses open parentheses 2 square root of 2 minus 3 close parentheses over denominator open parentheses 2 square root of 2 plus 3 close parentheses open parentheses 2 square root of 2 minus 3 close parentheses end fraction end cell row blank equals cell fraction numerator 3 minus 8 square root of 2 over denominator negative 1 end fraction end cell row blank equals cell fraction numerator 8 square root of 2 minus 3 over denominator 1 end fraction end cell row blank equals cell 8 square root of 2 minus 3 end cell end table end style$

Jadi, bentuk sederhana dari $fraction numerator square root of 2 plus 3 over denominator square root of 2 plus 1 end fraction plus fraction numerator 2 square root of 2 plus 1 over denominator 2 square root of 2 plus 3 end fraction plus fraction numerator square root of 2 plus 1 over denominator square root of 2 minus 1 end fraction$ .