Question

13. Se a e b são raízes da equação x² – 7x+1=0, então o valor da expressão (a-1)* +(6-1)" é:​

Answer 1

$\boxed{\begin{array}{l}\sf x^2-7x+1=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-7)^2-4\cdot1\cdot1\\\sf\Delta=49-4\\\sf\Delta=45\\\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-7)\pm\sqrt{45}}{2\cdot1}\\\\\sf x=\dfrac{7\pm3\sqrt{5}}{2}\begin{cases}\sf x_1=\dfrac{7+3\sqrt{5}}{2}\\\sf x_2=\dfrac{7-3\sqrt{5}}{2}\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf( a-1)+(6-1)\\\sf=\bigg(\dfrac{7+3\sqrt{5}}{2}-1\bigg)+5\\\sf\dfrac{7+3\sqrt{5}-2}{2}+\dfrac{10}{2}\\\sf =\dfrac{15+3\sqrt{5}}{2}\end{array}}$

Answer 2

Resposta:

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Explicação passo-a-passo:

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