If a,b,c are three sides of $$ riangle ABC$$, such that
$$a^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^2$$
Which kind of triangle best describes $$△ABC$$?

Question

If a,b,c are three sides of $$	riangle ABC$$, such that
$$a^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^2$$
Which kind of triangle  best describes $$△ABC$$?

Uniteasy Admin · Accepted Answer

$$a^4+b^4+c^4=a^2b^2+b^2c^2+c^2a^2$$
$$2a^4+2b^4+2c^4=2a^2b^2+2b^2c^2+2c^2a^2$$
$$2a^4+2b^4+2c^4-2a^2b^2-2b^2c^2-2c^2a^2=0$$
$$(a^2-b^2)^2+(b^2-c^2)^2+(a^2-c^2)^2=0$$
$$	herefore  $$
$$ (a^2-b^2)^2=0$$
$$(b^2-c^2)^2=0$$
Therefore, △ABC is an equilateral triangle.
C is the correct choice.
$$(a^2-c^2)^2=0$$
$$∴ a=b=c$$

Multiple Choice Question (MCQ)

Answer