Question

State true or false:

If $a,b\in +R$ and $a\ne b$ then, $a^4+b^4>a^{3}b+a{b}^3$.

• A. True
• B. False

Answer 1

The correct option is A True

Let the statment be true. i.e,

$a^4+b^4>a^{3}b+a{b}^3$

$a^4+b^4-a^{3}b-a{b}^3>0$

$a^3(a-b)-b^3(a-b)>0$

$(a^3-b^3)(a-b)>0$

$(a-b)(a^2+b^2-ab)(a-b)>0$

$(a-b{)}^2(a^2+b^2-ab)>0$

$(a-b{)}^2((a-b{)}^2+ab)>0$

This is true for $a\ne b,a,b\in R^{+}$

Hence our assumption was right.