Question

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$\it \Big|\sqrty5+\dfrac{x}{\sqrt5}\Big|=\sqrt{45}$

Answer 1

$|5 + \frac{x}{ \sqrt{5} } | = \sqrt{45} \\ |5 + \frac{x \sqrt{5} }{5} | = 3 \sqrt{5}$

Acum impartim in 2 cazuri posibile

I caz :

$5 + \frac{x \sqrt{5} }{5} = 3 \sqrt{5} \\ x = 15 - 5 \sqrt{5} \\ x = 5(3 - \sqrt{5})$

II caz :

$5 + \frac{x \sqrt{5} }{5} = - 3 \sqrt{5} \\ x = - 15 - 5 \sqrt{5} \\ x = - 5(3 + \sqrt{5})$

Answer 2

$|5+\frac{x}{\sqrt{5}}|=\sqrt{45}\\ \\|5+\frac{\sqrt{5}x}{5}|=3\sqrt{5}$

• ⁵⁾5 + √5x/5 = ⁵⁾3√5

25 + √5x = 15√5

√5x = 15√5 - 25

x = 15√5/√5 - 25/√5

x = 15 - 25/√5

x = 15 - 25√5/5

x₁ = 15 - 5√5

• ⁵⁾5 + √5x/5 = - ⁵⁾3√5

25 + √5x = - 15√5

√5x = - 25 - 15√5

x = - 15√5/√5 - 25/√5

x = - 15 - 25√5/5

x₂ = - 15 - 5√5