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  • Usuário do Brainly
2014-08-30T04:22:57-03:00
Olá, Diana !

Observe que:

a^2-b^2=(a+b)(a-b)

Se a=\dfrac{5+\sqrt{3}}{2} e b=\dfrac{5-\sqrt{3}}{2}, temos:

a^2-b^2=\left(\dfrac{5+\sqrt{3}}{2}+\dfrac{5-\sqrt{3}}{2}\right)\left(\dfrac{5+\sqrt{3}}{2}-\dfrac{5-\sqrt{3}}{2}\right)

a^2-b^2=\left(\dfrac{5+5+\sqrt{3}-\sqrt{3}}{2}\right)\left(\dfrac{5-5+\sqrt{3}+\sqrt{3}}{2}\right)

a^2-b^2=\left(\dfrac{10}{2}\right)\left(\dfrac{2\sqrt{3}}{2}\right)=5\cdot\sqrt{3}

a^2-b^2=5\sqrt{3}
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