+647 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.
((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
