If x+y=-4, then what is the value of x^{3}+y^ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the equation $x+y = -4$.Cubing both sides,we get $(x+y)^3 = (-4)^3$.Using the identity $(x+y)^3 = x^3 + y^3 + 3xy(x+y)$,we have $x^3 + y^3 +

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Given the equation $x+y = -4$.Cubing both sides,we get $(x+y)^3 = (-4)^3$.Using the identity $(x+y)^3 = x^3 + y^3 + 3xy(x+y)$,we have $x^3 + y^3 + 3xy(x+y) = -64$.Substitute the value of $(x+y) = -4$ into the equation:$x^3 + y^3 + 3xy(-4) = -64$.$x^3 + y^3 - 12xy = -64$.Adding $64$ to both sides,we get $x^3 + y^3 - 12xy + 64 = -64 + 64$.Therefore,$x^3 + y^3 - 12xy + 64 = 0$.

If $x+y=-4,$ then what is the value of $x^{3}+y^{3}-12xy+64?$

Similar Questions

Factorise: $49 a^{2}+70 a b+25 b^{2}$

If $x+y=12$ and $xy=27$,find the value of $x^{3}+y^{3}$.

Factorise the following: $27-125 a^{3}-135 a+225 a^{2}$

Prove that $(a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a).$

Verify: $x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module