E.684. Rezolvați ecuațiile: a) 7(x2+2)=98;7(x^2+\sqrt{2})=\sqrt{98};\qquad7(x2+2)=98; b) (x+3)2=27;(x+\sqrt{3})^2=27;\qquad(x+3)2=27;c) 4x2=(2+3)24x^2=(2+\sqrt{3})^24x2=(2+3)2.
a) 7(x2+2)=727(x^2+\sqrt{2})=7\sqrt{2}7(x2+2)=72 x2+2=2⇒x=0.x^2+\sqrt{2} = \sqrt{2} \Rightarrow \boxed{x=0}.x2+2=2⇒x=0.
b) x+3=±3⇒x1=0; x2=−23.x+\sqrt{3}=\pm\sqrt{3} \Rightarrow \boxed{x_1=0;~ x_2=-2\sqrt{3}}.x+3=±3⇒x1=0; x2=−23.
c x2=(2+32)2⇒x=±2+32.x^2=\Big(\dfrac{2+\sqrt{3}}{2}\Big)^2 \Rightarrow \boxed{x=\pm\dfrac{2+\sqrt{3}}{2}}.x2=(22+3)2⇒x=±22+3.