Question

Se A= √√6-2 . √(2+√6) então o valor de A²=?




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Answer 1

Resposta:

A²=2

Explicação passo-a-passo:

$A=\sqrt{(\sqrt{6} -2)(2+\sqrt{6} )} \\ \\ A=\sqrt{\sqrt{6}(2+\sqrt{6})-2.(2+\sqrt{6}   } \\ \\A=\sqrt{2\sqrt{6}+\sqrt{36} -4-2\sqrt{6}  }  \\ \\ A=\sqrt{\not2\sqrt{6}+6-4\not2\sqrt{6}  } \\ \\ A=\sqrt{6-4} \\ \\ A=\sqrt{2} \\ \\ Logo\\ \\ A^2=(\sqrt{2} )^2=2$