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slmt thn baru (xi)

[tex]\sqrt{7+2\sqrt{10}}=\sqrt{p}+\sqrt{q}\:\:\{p,q\in\rm Z\}[/tex]

p² + q² = ....

Answer 1

Verified answer

Jawab:

p²+q² = 29

Penjelasan dengan langkah-langkah:

[tex]\sqrt{7+2\sqrt{10} } =\sqrt{p} +\sqrt{q} \\7+2\sqrt{10} = ( \sqrt{p} +\sqrt{q})^{2} \\7+2\sqrt{10} = p +q +2\sqrt{pq}[/tex]

maka p+q = 7 lalu pq = 10

maka  p = 5 dan q = 2

maka p²+q² = 5²+2² = 25+4 = 29

Answer 2

Jawaban:

29

Penjelasan dengan langkah-langkah:

[tex]

\sqrt{7+2\sqrt{10}}=\sqrt{p}+\sqrt{q}\:\:\{p,q\in\rm Z\}

\\ (

\sqrt{7+2\sqrt{10}} {)}^{2} =(\sqrt{p}+\sqrt{q} {)}^{2} \:\:

\\ 7 + 2 \sqrt{10} = p + 2 \sqrt{pq} + q \\ \boxed{7 + 2 \sqrt{2 \times 5}\to(2 + 2 \sqrt{2 \times 5} + 5 } \\ 2 + 5 + 2 \sqrt{2 \times 5} = p + q + 2 \sqrt{pq} \\ p + q = 2 + 5 \\ \\ maka \: \\ {2}^{2} + {5}^{2} = 4 + 25 \\ = 29[/tex]

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