x²-2x-m=0 Jika X₁ dan X₂ akar-akar Pk dan x₁² - x²=16 Tentukan m
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Jawaban:
m = 15
Penjelasan dengan langkah-langkah:
x² - 2x - m = 0
x₁² - x₂² = 16
x₁² - x₂² = (x₁ - x₂)(x₁ + x₂)
[tex]x1 - x₂ = \frac{ \sqrt{d} }{a} = \frac{ \sqrt{4 + 4m} }{1} = \sqrt{4 + 4m} [/tex]
[tex] \sqrt{4 + 4m} = \sqrt{4(1 + m)} = 2 \sqrt{(m + 1)} [/tex]
x₁ + x₂ = -b/a = 2
x₁² - x₂² = (x₁ - x₂)(x₁ + x₂) = 16
[tex](2 \sqrt{(m + 1)} )(2) = 16[/tex]
[tex]2 \sqrt{(m + 1)} = 8[/tex]
[tex]4(m + 1) = 64[/tex]
[tex]m + 1 = \frac{64}{4} [/tex]
[tex]m + 1 = 16[/tex]
[tex] \boxed{m = 15}[/tex]
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