Question

if X + i y whole cube equals to u + IV then show that you divided by X + we divided by y equals to 4 x square minus y square​

Answer 1

u/x  + v/y  = 4(x² - y²)  if  (x + iy)³ = u + iv

Step-by-step explanation:

(x + iy)³ = u + iv

x³  + (iy)³   + 3x²(iy)  + 3x(iy)²  = u + iv

=> x³  - iy³  + i 3x²y  - 3xy² = u + iv

=> x³ - 3xy²  + i (3x²y - y³) = u + iv

=> x(x² - 3y²)  + iy(3x² - y²)  = u + iv

u =  x(x² - 3y²)

=> u/x = x² - 3y²

v = y(3x² - y²)

=> v/y = 3x² - y²

u/x  + v/y  = x² - 3y²  + 3x² - y²

=> u/x  + v/y  = 4x² - 4y²

=>  u/x  + v/y  = 4(x² - y²)

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