Question

If 2x⁴,2y⁴,2z⁴=144,then find the mean of x⁴,y⁴,z⁴.

Answer 1

$\text{Given that,}\\\\~~~~~~~2x^4 +2y^4 +2z^4 = 144\\\\\implies 2(x^4+y^4 +z^4) = 144\\\\\implies x^4 +y^4 +z^4 = \dfrac{144}{2}\\\\\implies x^4 +y^4 +z^4 = 72\\\\\text{Mean} = \dfrac{x^4+y^4+z^4}{3}\\\\~~~~~~~~=\dfrac{72}{3}\\\\~~~~~~~~=24$