Multiple Choice Question (MCQ)

If x + y + z = 10, x^3+y^3+z^3=75 and xyz=15, then find the value of x^2+y^2+z^2−xy−yz−zx

  1. ×

    4

  2. 3

  3. ×

    5

  4. ×

    6

Collected in the board: The сube of sum

Steven Zheng posted 2 weeks ago

Answer

  1. Using the identity

    x^3+y^3+z^3−3xyz = (x+y+z)( x^2+y^2+z^2−xy−yz−zx)

    The expression can be expressed

    x^2+y^2+z^2−xy−yz−zx = \dfrac{x^3+y^3+z^3−3xyz}{x+y+z} = \dfrac{75-3\cdot 15}{10} =3

Steven Zheng posted 2 weeks ago

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