Resposta:

y.z² = -0.880000...

Explicação passo a passo:

y =[tex]\frac{[(0,2525... - \frac{2}{3}) : (\frac{16}{33} + 0,3434...)]^{-1} }{1,2 + \frac{4}{5} }[/tex]

z = [tex]\sqrt{\frac{20^{30} +2^{29}}{2^{29} + 2^{28}}}[/tex]

Vamos começar calculando o valor de z:

z = √(20³⁰+2²⁹) / (2²⁹ + 2²⁸)

z = √(2⁶⁰ + 2⁵⁹) / (2²⁸ x 3)

z = √(2⁵⁹ x (2 + 1)) / (2²⁸ x 3)

z = √(2⁵⁹) x √(2 + 1) / (2²⁸ x 3)

z = 2²⁹ x √3 / (2²⁸ x 3)

z = 2 x √3 / 3

Agora, podemos calcular o valor de y:

[tex]y = \frac{[(0,2525... - \frac{2}{3}) : (\frac{16}{33} + 0,3434...)]^{-1} }{1,2 + \frac{4}{5} }\\y = \frac{[(0.2525252525... - 0.666666...): (1.87878787...)]^{-1}}{1.2 + 0.8}\\y = \frac{(-0.414141...)/(1.87878787...)^{-1}}{2}\\y = \frac{-0.414141...}{1.87878787...} x \frac{1}{2}\\y = -0.220000...[/tex]

Finalmente, podemos calcular o valor de y.z²:

y.z² = -0.220000... x (2 x √3 / 3)²

y.z² = -0.220000... x (4/9 x 3)

y.z² = -0.220000... x 4

y.z² = -0.880000...

Portanto, y.z² é aproximadamente igual a -0,8800.

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