Find the value of i. x³ + y³ - 12xy + 64, when x + y = - 4 Class 9

Find the value of i. x³ + y³ - 12xy + 64, when x + y = - 4 Class 9

Question 1.

Find the value of

i. x³ + y³ - 12xy + 64, when x + y = - 4 Class 9

ii. x³ - 8y³ - 36xy - 216, when x = 2y + 6

Solution:

x³ + y³ - 12xy + 64

= x³ + y³ + 64 - 12xy

= x³ + y³ + 4³ - 3(x)(y)(4)

= (x + y + 4)(x² + y² + 16 - xy - 4x - 4y)

...[∵ a³ + b³ + c³ - 3 abc

= (a + b + c) (a² + b² + c² - ab - bc - ac)]

= (- 4 + 4)(x² + y² + 16 - xy - 4x - 4y) = 0

...[∵ x + y = -4]

ii. x³ - 8y³ - 36xy - 216

= x³ - 8y³ - 216 - 36xy

= x³ + (-2y)³ + (-6)³ - 3(x)(-2y)(-6)

= [x + (-2y) + (-6)] [x² + (-2y)² + (-6)² - x(-2y) - x(-6) - (-2y)(-6)]

...[∵ a³ + b³ + c³ - 3abc

= (a + b + c) (a² + b² + c² - ab - bc - ac)]

= (x - 2y - 6) (x² + 4y² + 36 + 2xy + 6x - 12y)

= (2y + 6 - 2y - 6)(x² + 4y² + 36 + 2xy + 6x - 12y)

.....[∵ x = 2y + 6]

= 0