Question

If x+y=12 and xy =32 find the value of x³+y³

Answer 1

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$

(x + y) = 12

xy = 27

Using Identity

x^3 + y^3 = (x + y)^3 - 3xy(x + y)

⇒ x^3 + y^3 = (12)^3 - 3(27)(12)

⇒ x^3 + y^3 =  1728 - 972

⇒ x^3 + y^3 = 756

$\bf\huge\bf\huge{\boxed{\bigstar{{x^3 + y^3 = 756}}}}$

Answer 2

$x^{3}+y^{3}= 756$

given = x+y = 12

xy=32

to find :- x^{3}+y^{3}

x+y = 12 (cubing on both side)

$x^{2}+y^{3}=(x+y)^{3} -3xy(x+y) \\ x^{3}+y^{3} = 12^{3}- 3 (32)(12) \\ x^{3}+y^{3} = 756$