Плагиат предупреждение.Спам предупреждение................1111111. Created by DHAcity. algebra-ru

Плагиат предупреждение.Спам предупреждение................1111111...

nKrynka $1)\; \; x^4-7x^2+6=0\; ,\; \; \; t=x^2 \geq 0\\\\t^2-7t+6=0\; \; \to \; \; t_1=1\; ,\; t_2=6\; \; (teorema\; Vieta)\\\\x^2=1\; \; \; \to \; \; \; x=\pm 1\\\\x^2=6\; \; \; \to \; \; \; x=\pm \sqrt6\\\\Otvet:\; \; -1\; ,\; -\sqrt6\; ,\; 1\; ,\; \sqrt6\; .\\\\2)\; \; x^4+3x^2-4=0\; ,\; \; \; \; t=x^2 \geq 0\\\\t^2+3t-4=0\; \; \to \; \; \; t_1=-4\ \textless \ 0\; ,\; t_2=1\\\\x^2=1\; \; \; \Rightarrow \; \; \; x=\pm 1$

$3)\; \; x^4+5x^2+9=0\; ,\; \; \; \; t=x^2 \geq 0\\\\t^2+5t+9=0\\\\D=25-4\cdot 9=-11\ \textless \ 0\; \; \to \; net\; reshenij\\\\x\in \varnothing$

$4)\; \; x^4-5x^2+4=0\; ,\; \; \; \; t=x^2 \geq 0\\\\t^2-5t+4=0\; \; \to \; \; \; t_1=1\; ,\; \; t_2=4\\\\x^2=1\; \; \; \to \; \; \; x=\pm 1\\\\x^2=4\; \; \; \to \; \; \; x=\pm 2\\\\Otvet:\; \; -1\; ,\; 1\; ,\; -2\; ,\; 2\; .$

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Verified answer

Решение
а) x⁴ - 7x² + 6 = 0
x² = t
t² - 7t + 6 = 0
t₁ = 1
t₂ = 6
1) x² = 1
x₁ = - 1
x₂ = 1
2) x² = 6
x₃ = - √6
x₄ = √6

б) x⁴ + 3x² - 4 = 0
x² = t, t ≥ 0
t² + 3t - 4 = 0
t₁ = - 4, не удовлетворяет условию t ≥ 0
t₂ = 1
x² = 1
x₁ = - 1
x₂ = 1

в) x⁴ + 5x + 9 = 0
x² = t
t² + 5t + 9 = 0
D = 25 - 4*1*9 = - 11 < 0, решений нет

г) x⁴ - 5x + 4 = 0
x² = t
t² - 5t + 4 = 0
t₁ = 1
t₂ = 4
1) x² = 1
x₁ = - 1
x₂ = 1
2) x² = 4
x₃ = - 2
x₄ = 2

2 votes Thanks 1

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reshit4e30ab47328f21c49bf4f68a7d2d2e8a 66496

reshitd053827f699ebce6f3d63a3723110647 59680

reshit7d0400b9b683362a68cb02adb02fd1a8 2181

srochno5a90ed8dd1b9ec73e25fa066756297e7 17779

reshit288e983d7a132755e3aae800079ab368 37217

srochnocd63a0ef0141f9b9c01fd84576602411 89406

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reshit172b7c182f06c890d1036a82b8dea0aa 20631

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