Question

$if \: x + y = 12 \: and \: xy = 27 \: find \: {x}^{3} + {y}^{3}$
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Answer 1

Hey♥️

xy = 27

$x = \frac{27}{y} \: \: \: \: \: \: (i)$

x + y = 12. ....(ii)

Substituting (i) in (ii), we get,

$\frac{27}{y} + y = 12$

(or) y² - 12y + 27 = 0

y² - 3y - 9y + 27 =0

y(y - 3) -9 (y - 3) =0

(y - 9) ( y - 3) =0

Therefore, y= 9 or y = 3

If y= 9, in (i)

$x = \frac{27}{9} \\ x = 3$

If y= 3 , in (i)

$x = \frac{27}{9} \\ x = 3$

x³ + y³

= 3³ + 9³

= 756

Answer 2

Answer:

→  x³ + y³ = 756

Step-by-step explanation:

Given,

x + y = 12

xy = 27

To find the x³ + y³

Formula :

x³ + y³ = (x + y)³ - 3xy (x + y)

x³ + y³ =  (12)³ - 3 (27) (12)

x³ + y³ = 1728 - 972

x³ + y³ = 756.

∴x³ + y³ = 756.

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