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If  \(z = \frac{ \left\{ \sqrt{3} \right\}^2 - 2 \left\{ \sqrt{2} \right\}^2 }{ \left\{ \sqrt{3} \right\} - 2 \left\{ \sqrt{2} \right\} }\)find z.

 Mar 15, 2018
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((sqrt(3))^2 - 2 (sqrt(2))^2)/(sqrt(3) - 2 sqrt(2))=z

 

Multiply exponents. (sqrt(2))^2 = 2^(2/2):

((sqrt(3))^2 - 22^(2/2))/(sqrt(3) - 2 sqrt(2))

 

((sqrt(3))^2 - 2×2)/(sqrt(3) - 2 sqrt(2))

 

Cancel exponents. (sqrt(3))^2 = 3:

(3 - 2×2)/(sqrt(3) - 2 sqrt(2))

 

(-4 + 3)/(sqrt(3) - 2 sqrt(2))

 

(-1)/(sqrt(3) - 2 sqrt(2))

 

Multiply numerator and denominator of (-1)/(sqrt(3) - 2 sqrt(2)) by -1:

1/(2 sqrt(2) - sqrt(3))

 

Multiply numerator and denominator of 1/(2 sqrt(2) - sqrt(3)) by 2 sqrt(2) + sqrt(3):

(2 sqrt(2) + sqrt(3))/((2 sqrt(2) - sqrt(3)) (2 sqrt(2) + sqrt(3)))

 

(2 sqrt(2) - sqrt(3)) (2 sqrt(2) + sqrt(3)) = 2 sqrt(2)×2 sqrt(2) + 2 sqrt(2) sqrt(3) - sqrt(3)×2 sqrt(2) - sqrt(3) sqrt(3) = 8 + 2 sqrt(6) - 2 sqrt(6) - 3 = 5:

 

z = (2sqrt(2) + sqrt(3)) / 5

 Mar 15, 2018

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