Question

Considerando $\sqrt{2} = 1,41$ e $\sqrt{3} = 1,73$ , determine a solucao aproximada com duas casas decimais de cada equacao.

a) $3x=2x+2\sqrt{2}$
b)$8x-2=7x+\sqrt{3}$


OBS: Nao usar forma de baskhara (equacao segundo grau)

Answer 1

Resposta:

Vejamos as resoluções:

A ) 3x = 2x + 2√2

3x = 2x + 2 . 1,41

3x - 2x = 2,82

x = 2,82

B ) 8x - 2 = 7x + √3

8x - 2 = 7x + 1,73

8x - 7x = 1,73 + 2

x = 3,73

Answer 2

$\sf 3x=2x+2\sqrt{2}\\\\\\\\\sf 3x=2x+2\ll para ~1,41 \\\\\\\\\sf 3x=2x+2\cdot \:1.41\\\\\\\\\boxed{ \sf Multiplicar\:os\:n\acute{u}meros\:2\cdot \:1.41=2.82}\\\\\\\\\sf 3x=2x+2,82\\\\\\\\\sf \boxed{\sf Subtrair\:2x\:de\:ambos\:os\:lados}\\\\\\\\\sf 3x-2x=2x+2.82-2x\\\\\\\\\boxed{\sf Simplificar}\\\\\\\\\boxed{\sf S_1=\{2,82\}}$

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$\sf 8x-2=7x+\sqrt{3} \\\\\\\\\sf 8x-2=7x+\sqrt{3}\ll~para~1,73\\\\\\\\ \sf 8x-2=7x+1,73\\\\\\\\\sf \boxed{\sf Adicionar\:2\:a\:ambos\:os\:lados}\\\\\\\\\sf 8x-2+2=7x+1,73+2\\\\\\\\\boxed{\sf Simplificar }\\\\\\\\\sf 8x=7x+3,73\\\\\\\\\boxed{\sf Subtrair\:7x\:de\:ambos\:os\:lados}\\\\\\\\\sf 8x-7x=7x+3,73-7x\\\\\\\\\sf \boxed{\sf Simplificar }\\\\\\\\\boxed{\sf S_2=\{3,73\}}$