Question

if x+y = a and x2+y2 = b then find the value of x3+y3

Answer 1

x+y =a

on squaring both sides

(x+y) ^2=a^2

x^2+y^2+2xy =a^2

b+2xy=a^2

2xy=a^2-b

xy =(a^2-b) /2

Now, x^3+y^3

=(x+y) ( x^2+y^2-xy)

=a×{b-( a^2-b)/2}

=a×(2b-a^2+b)/2

=(2ab-a^3+ab)/2

Answer 2

Answer:

$hello$

we know,

the algebraic formula

☑ (a^3+b^3)=(a+b)(a^2-ab+b^2)

therefor ,

(x^3+y^3)= (x+y)(x^2-xy+y^2)

we have,

x+y=a

x^2+y^2 = b

xy = ?

☑ the algebraic formula,

(a+b)^2= a^2+2ab+b^2

(x +y)^2 =2xab+(x^2+x^2)

[(x+y)^2-(x^2+y^2)]/2 = (xy)

[(a)^2-(b) ]/2 = (xy)

☑ (x^3+y^3)= (x+y)(x^2-xy+y^2)

= (a) ((x^2+y^2)-(xy))

= (a) (b) -[(a) ^2-(b) ]/2