Răspuns:
Nu stiu cine ti-a spus ca raspunsul este varianta c) , deoarece raspunsul este a).
Explicație pas cu pas:
Hai sa simplificam putin radicalii inainte de a evalua toata expresia.
Asadar:
[tex]\sqrt[3]{x\sqrt{x} } = \sqrt[3]{(\sqrt{x})^2\sqrt{x} } = \sqrt[3]{(\sqrt{x})^3} = \sqrt{x}[/tex]
apoi
[tex]\sqrt[6]{y^2x} + \sqrt{x} = \sqrt[6]{y^2}*\sqrt[6]{x} + \sqrt[6]{x^3} = \sqrt[3]{y}*\sqrt[6]{x} + \sqrt[6]{x^2}*\sqrt[6]{x} = \sqrt[3]{y}*\sqrt[6]{x} + \sqrt[3]{x}*\sqrt[6]{x} = \sqrt[6]{x}( \sqrt[3]{y} + \sqrt[3]{x})[/tex]
asadar:
[tex]\frac{\sqrt[6]{y^2x} + \sqrt{x} }{\sqrt[3]{x} + \sqrt[3]{y}} + \sqrt[6]{x}= \frac{\sqrt[6]{x}( \sqrt[3]{y} + \sqrt[3]{x})}{{\sqrt[3]{y} + \sqrt[3]{x}} } +\sqrt[6]{x}= \sqrt[6]{x} + \sqrt[6]{x} = 2*\sqrt[6]{x}[/tex]
Deci expresia noastra devine( o notam cu A):
[tex]A = (\sqrt{x} + 1)^2 + 4(x + 1 ) + (2*\sqrt[6]{x})^3 = (\sqrt{x} + 1)^2 + 4x + 4 + 8*(\sqrt[6]{x})^3 = \\\\=(\sqrt{x} + 1)^2 + 4*(\sqrt{x})^2 +4 + 8*\sqrt{x} = (\sqrt{x} + 1)^2 + 4[(\sqrt{x})^2 +2*\sqrt{x} + 1] =\\\\= (\sqrt{x} + 1)^2 + 4 (\sqrt{x} + 1)^2= 5*(\sqrt{x} + 1)^2[/tex]
