Question

if,a+b=p ,a^(2)+b^(2)=q and a^(3)+b^(3)=r^(3).than show that,p^(3)+2r^(3)=3pq

Answer 1

Answer:

See explanation

Step-by-step explanation:

Given

          $a+b=p,a^2+b^2=q,a^3+b^3=r^3$

• Using  $(a+b)^2=a^2+b^2+2ab$

          $\Rightarrow p^2=q+2ab\\\Rightarrow ab=\frac{1}{2}(p^2-q)$  

• Now using $(a+b)^3=a^3+b^3+3ab(a+b)$

            $\Rightarrow p^3=r^3+3(\frac{1}{2}(p^2-q))p\\\Rightarrow 2p^3=2r^3+3p^3-3pq\\\Rightarrow p^3+2r^3=3pq$

Hence proved