Question

If x+y=5 then find value of x^3+y^3+15xy

Answer 1

(x+y)3 = x3 + y3 + 3xsqy + 3xysq

125 = x3 + y3+ 3xy(x + y)

125 = x3 + y3+ 3xy(5)

125 = x3 + y3+ 15xy

x3 + y3+ 15xy - 125 = 0

x+y=5

cubing on both sides

(x+y)^3=125

x^3+y^3+3xy(x+y)=125

x^3+y^3+3xy(5)=125. (Since x+y=5)

x^3+y^3+15xy=125

Thus

x^3+y^3+15xy-125=0

Answer 2

x^3+y^3+15xy
=(x+y)^3+3xy(x+y)+15xy
=(5)^3-3xy(5)+15xy [x+y=5]
=125