Question

plz solve this question quick plz​

Answer 1

x+y= a

x^2 + y^2 = b

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

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

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

= a^2 - b)/2

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

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

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

= a( 2 b - a^2 + b)/2

= a( 3b - a^2)/2

= 3ab - a^3 )/2

(D) is correct

Answer 2

We know that x+y=a and x∧2+y∧2=b

First we have to find xy by using (x+y)∧2

⇒ (x+y)∧2=x∧2+y∧2+2xy

⇒ a∧2=b+2xy

⇒ a∧2-b/2=xy

Now use x∧3+y∧3

⇒ x∧3+y∧3=(x+y)(x∧2-xy+y∧2

   x∧3+y∧3=a(b-a∧2+b/2)

   x∧3+y∧3=a(2b-a∧2+b/2)

   x∧3+y∧3=2ab-a∧3+ab/2

   x∧3+y∧3=3ab-a∧3/2