Question

find the value of x³ + y³ + 12xy = 64 , when x + y = 4​

Answer 1

Step-by-step explanation:

a

3

+b

3

+c

3

=(a+b+c)(a

2

+b

2

+c

2

−ab−bc−ca)+3abc

If a+b+c=0, then a

3

+b

3

+c

3

=3abc

Now, given x

3

+y

3

−12xy+64 and

x+y=−4

=>x+y+4=0

Here, a=x, b=y, c=4 and a+b+c=x+y+4=0

Therefore

x

3

+y

3

+64=3xy(4)

=12xyz

Now,

x

3

+y

3

+64−12xyz=12xyz−12xyz

=0

Answer 2

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$\implies$$\large\bf{\underline{\red{VERIFIED✔}}}$

x³+y³ + 12xy - 64

x³+y³-43 + 3(4xy) [ By (64=4³) ]

(x + y - 4)(x² + y² + 4² - xy - 4y - 4x)

x + y = + 4

(4+4) (x² + y² + 4² - xy - 4y - 4x)

O* (x² + y² + 4² - xy - 4y - 4x)

= 0.

• I Hope it's Helpful My Friend.