номер 8.50, 2. ответ должен получиться 105.. Created by anjekawolf. algebra-ru

номер 8.50, 2. ответ должен получиться 105...

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X² - 12x +13 = 0
По теореме Виета
x₁ * x₂ = 13 x₁ + x₂ = 12

x₁³ + x₂³ = (x₁ + x₂)(x₁² - x₁ * x₂ + x₂²)

(x₁ + x₂)² = 12²
x₁² + 2x₁x₂ + x₂² = 144
x₁² + x₂² = 144 - 2x₁ * x₂
x₁² + x₂² = 144 - 2 * 13 = 144 - 26 = 118

x₁³ + x₂³ = 12 * (118 - 13) = 12 * 105
$\frac{1}{12} ( x_{1} ^{3} + x_{2} ^{3})= \frac{1}{12}*12*105=105$

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yarynahrytsiv

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$x^{2} -12x+13=0 \\ \left \{ {{x_{1} * x_{2} =13} \atop x_{1} + x_{2} =12}} \right. \\ 
 \frac{1}{12} *( x^{3} _{1}+ x^{3} _{2})= \frac{1}{12} *((x _{1}+ x _{2})^{3}-3*x _{1}* x _{2}*(x _{1}+ x _{2}))= \\ =\frac{1}{12} *(12^{3}-3*13*12)=105$

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