Question

find the value of x² + y² + 15 xy - 125 if x+y = 5​

Answer 1

Given, (x+y)=5

Cubing both sides,

x^3 +y^3 +3x^2y +3xy^2=125

Adding 15xy to both the sides,

x^3 +y^3 -125 + 15xy = -3xy^2 -3x^2y +15xy

=>x^3 +y^3 -125 +15xy =3xy(-(y+x) +5).....................(substituting the value of (x+y))

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

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

So, the answer of the given expression is zero