Question

2
.
Hallar La suma de las raíces son:
$\sqrt[3]{5 - x} + \sqrt[3]{x + 4} = 3$
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Answer 1

Respuesta:

x = -3

x = 4

Explicación paso a paso:

$\sqrt[3]{5 - x} + \sqrt[3]{x + 4} = 3$

${(\sqrt[3]{5 - x} + \sqrt[3]{x + 4} ) }^{3} = {3}^{3}$

$(5 - x) + (x + 4) + 3\sqrt[3]{5 - x}\sqrt[3]{x + 4} ( \sqrt[3]{5-x}+\sqrt[3]{x+4} )= 27$

$9+ 3\sqrt[3]{-x^2 + x +20} ( 3 )= 27$

$9+ 9\sqrt[3]{-x^2 + x +20} = 27$

$1+ \sqrt[3]{-x^2 + x +20} = 3$

$\sqrt[3]{-x^2 + x +20} = 3-1$

$\sqrt[3]{-x^2 + x +20} = 2$

$-x^2 + x +20 = 8$

$-x^2 + x +12 = 0$

$x^2 - x - 12 = 0$

$(x-4)(x+3) = 0$

x = -3

x = 4