Pertanyaan

Nyatakan 2 − 5 2 + 5 dalam bentuk p + q dimana p dan q adalah bilangan bulat. Kemudian tentukan nilai dari ( 2 − 5 2 + 5 ) 2 + ( 2 + 5 2 − 5 ) 2 .

Nyatakan $\frac{2 + 5}{2 - 5}$ dalam bentuk $p + q$ dimana $p dan q$ adalah bilangan bulat. Kemudian tentukan nilai dari $(\frac{2 + 5}{2 - 5})^{2} + (\frac{2 - 5}{2 + 5})^{2}$ .

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Jawaban terverifikasi

Jawaban

nilai dari adalah 322.

nilai dari $open parentheses fraction numerator 2 plus square root of 5 over denominator 2 minus square root of 5 end fraction close parentheses squared plus open parentheses fraction numerator 2 minus square root of 5 over denominator 2 plus square root of 5 end fraction close parentheses squared$ adalah 322.

Pembahasan

Ingat kembali bahwa: Menyatakan dalam bentuk : Menyatakan dalam bentuk : Menentukan nilai dari operasi hitung bentuk akar: Jadi,nilai dari adalah 322.

Ingat kembali bahwa:

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

Menyatakan $fraction numerator 2 plus square root of 5 over denominator 2 minus square root of 5 end fraction$ dalam bentuk p plus square root of q :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 plus square root of 5 over denominator 2 minus square root of 5 end fraction end cell equals cell fraction numerator 2 plus square root of 5 over denominator 2 minus square root of 5 end fraction cross times fraction numerator 2 plus square root of 5 over denominator 2 plus square root of 5 end fraction end cell row blank equals cell fraction numerator 4 plus 2 square root of 5 plus 2 square root of 5 plus 5 over denominator 2 squared minus open parentheses square root of 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 9 plus 4 square root of 5 over denominator 4 minus 5 end fraction end cell row blank equals cell fraction numerator 9 plus 4 square root of 5 over denominator negative 1 end fraction end cell row blank equals cell negative 9 minus 4 square root of 5 end cell end table$

Menyatakan $fraction numerator 2 minus square root of 5 over denominator 2 plus square root of 5 end fraction$ dalam bentuk p plus square root of q :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 minus square root of 5 over denominator 2 plus square root of 5 end fraction end cell equals cell fraction numerator 2 minus square root of 5 over denominator 2 plus square root of 5 end fraction cross times fraction numerator 2 minus square root of 5 over denominator 2 minus square root of 5 end fraction end cell row blank equals cell fraction numerator 4 minus 2 square root of 5 minus 2 square root of 5 plus 5 over denominator 2 squared minus open parentheses square root of 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 9 minus 4 square root of 5 over denominator 4 minus 5 end fraction end cell row blank equals cell fraction numerator 9 minus 4 square root of 5 over denominator negative 1 end fraction end cell row blank equals cell 4 square root of 5 minus 9 end cell end table$

Menentukan nilai dari operasi hitung bentuk akar:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses fraction numerator 2 plus square root of 5 over denominator 2 minus square root of 5 end fraction close parentheses squared plus open parentheses fraction numerator 2 minus square root of 5 over denominator 2 plus square root of 5 end fraction close parentheses squared end cell row blank equals cell open parentheses negative 9 minus 4 square root of 5 close parentheses squared plus open parentheses 4 square root of 5 minus 9 close parentheses squared end cell row blank equals cell open parentheses open parentheses negative 9 close parentheses squared plus 2 open parentheses negative 9 close parentheses open parentheses negative 4 square root of 5 close parentheses plus open parentheses negative 4 square root of 5 close parentheses squared close parentheses plus open parentheses open parentheses 4 square root of 5 close parentheses squared minus 2 open parentheses 4 square root of 5 close parentheses open parentheses 9 close parentheses plus 9 squared close parentheses end cell row blank equals cell open parentheses 81 plus 72 square root of 5 plus 80 close parentheses plus open parentheses 80 minus 72 square root of 5 plus 80 close parentheses end cell row blank equals 322 end table$

Jadi, nilai dari $open parentheses fraction numerator 2 plus square root of 5 over denominator 2 minus square root of 5 end fraction close parentheses squared plus open parentheses fraction numerator 2 minus square root of 5 over denominator 2 plus square root of 5 end fraction close parentheses squared$ adalah 322.