Question

Care este suma solutiilor reale ale ecuatiei $\sqrt[3]{x} +2\sqrt[3]{x^{2} } = 3$ ?

Answer 1

Explicație pas cu pas:

$\sqrt[3]{x}+2\sqrt[3]{x^2} =3 \\(\sqrt[3]{x}+2\sqrt[3]{x^2})^{3} =27\\(x+3*\sqrt[3]{x^2} *2\sqrt[3]{x^2} +3*\sqrt[3]{x} *4*\sqrt[3]{x^4} +8x^2)=27\\(x+3*\sqrt[3]{x^2} *2\sqrt[3]{x^2} +3*\sqrt[3]{x}*4*x\sqrt[3]{x} +8x^2)=27\\(x+6\sqrt[3]{x^4} +12\sqrt[3]{x}*x\sqrt[3]{x}+8x^2)=27\\(x+6*x\sqrt[3]{x} +12\sqrt[3]{x}*x\sqrt[3]{x}+8x^2)=27\\x+6x(\sqrt[3]{x} +2\sqrt[3]{x^2} )+8x^2=27\\x+6x*3+8x^2=27\\19x+8x^2-27=0\\8x^2+19x-27=0\\8x^2+27x-8x-27=0\\(8x^2-8x)+(27x-27)=0\\   </p><p>8x(x-1)+27(x-1)=0$

(8x+27)(x-1)=0

x₁=-27/8

x₂=1

S=-27/8+1=(-27+8)/8=-19/8-suma solutiilor.

Bafta!