Multiple Choice Question (MCQ)

If a,b,c are three sides of \triangle 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?

  1. ×

    Right triangle

  2. ×

    Isosceles triangle

  3. Equilateral triangle

  4. ×

    Acute triangle

Collected in the board: Triangle

Steven Zheng posted 21 hours ago

Answer

  1. 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

    \therefore

    (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

Steven Zheng posted 21 hours ago

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