Question

If x minus y is equal to 5 and x y is equal to 84 then find the value of x cube minus y cube

Answer 1

The value of x cube minus y cube is 1385.

• Given,

x - y = 5  - (i)

xy = 84  

=> y = 84 / x  -(ii)

• Putting the value of y as 84 / x in equation (i), we get,

x - (84 / x) = 5

Or, ( x² - 84 ) / x = 5

Or, x² - 84 = 5x

Or, x² - 5x - 84 = 0   [ Quadratic equation ]

Or, x² - 12x + 7x - 84 = 0

Or, x ( x - 12 ) + 7 ( x - 12 ) = 0

Or, ( x - 12 ) ( x + 7 ) = 0

Or, x - 12 = 0  ;  x + 7 = 0

Or, x = 12   ;    x = -7

• Putting the values of x in equation (ii), we get,

y = 84 / 12  ; y = 84 / -7

Or, y = 7   ; y = -12

• Now, the cube of x =  (12)³   ;   (-7)³

Or,  x³ = 1728  ;  x³ = -343

y³ = 7³  ;  (-12)³

Or, y³ = 343  ;   y³ = -1728

•    For  x³ = 1728,   y³ = 343 .

Therefore, x³ - y³ = 1728 - 343 = 1385

For  x³ = -343,    y³ = -1728 .

Therefore, x³ - y³ = -343 - (-1728)

Or, x³ - y³ = -343 + 1728 = 1385

•  ∴  The value of x³ - y³ = 1385

Answer 2

Step-by-step explanation:

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