Question

Cum se face? help. am nevoie pana la 12:00

Answer 1

$Fie \ \sqrt{3}+\sqrt{7}=x, \ atunci: \\ (\sqrt{3}+\sqrt{7}-\sqrt{11})(\sqrt{3}+\sqrt{7}+\sqrt{11})+(\sqrt{3}-\sqrt{7})^2= \\ =(x-\sqrt{11})(x+\sqrt{11})+(\sqrt{3}-\sqrt{7})^2 = x^2-\sqrt{11}^2+(\sqrt{3}-\sqrt{7})^2= \\ =(\sqrt3+\sqrt7)^2-11+(\sqrt3-\sqrt7)^2= \\ =\sqrt3^2+2\cdot\sqrt3\cdot\sqrt7+\sqrt7^2-11+\sqrt3^2-2\cdot\sqrt3\cdot\sqrt7+\sqrt7^2= \\ =3+2\sqrt{21}+7-11+3-2\sqrt{21}+7=10-11+3+7=2+7=\boxed{\bold{9}}$