Oblicz wartość wyrażenia [latex](a+b)^2 [/latex] dla [latex]a=sqrt{8-2sqrt{7}} i b=sqrt{8+2sqrt{7}}[/latex].

[latex](sqrt{8-2sqrt{7}}+sqrt{8+2sqrt{7}})^{2} = \ = (sqrt{8-2sqrt{7}})^{2}+(2*sqrt{8-2sqrt{7}}*sqrt{8+2sqrt{7}})+(sqrt{8+2sqrt{7}})^{2} = \[/latex] [latex]= (sqrt{8-2sqrt{7}})^{2}+(2*sqrt{8-2sqrt{7}}*sqrt{8+2sqrt{7}})+(sqrt{8+2sqrt{7}})^{2} = \ = (8-2sqrt{7})+(2*sqrt{(8-2sqrt{7})*(8+2sqrt{7})})+(8+2sqrt{7} ) = \[/latex] [latex]= (8-2sqrt{7})+(2*sqrt{(8-2sqrt{7})*(8+2sqrt{7})})+(8+2sqrt{7} ) = \ = 8-2sqrt{7}+2*(sqrt{64-28})+8+2sqrt{7} = \ = 16+2*sqrt{36} = 16+2*6 = 16+12 = 28[/latex]

[latex](sqrt{8 - 2sqrt{7}})^{2} + (2 * sqrt{8 - 2sqrt{7}} * sqrt{8 + 2sqrt{7}}) + sqrt{8 + 2sqrt{7}})^{2} = (8 -2sqrt{7}) +(2 * sqrt{(8 -2sqrt{7}) * (8 +2sqrt{7})}) + (8 +2sqrt{7}) = 16 + 2 * sqrt{64 - 28} = 16 + 2 * sqrt{36} = 16 + 26 = 28[/latex]

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