The difference between the maximum real root and the minimum real root of the equation $(x^2 - 5)^4 + (x^2 - 7)^4 = 16$ is

Question

Accepted Answer

D - $2\sqrt{7}$. Let t=x^2-6: (t+1)^4+(t-1)^4=2t^4+12t^2+2=16, so t^4+6t^2-7=0, t^2=1, x^2=5 or 7. Roots +-sqrt5, +-sqrt7; difference max-min = 2sqrt7.

Answer

A - $\sqrt{10}$

Answer

B - $2\sqrt{5}$

Answer

C - $\sqrt{7}$

The difference between the maximum real root and the minimum real root of the equation \((x^2 - 5)^4 + (x^2 - 7)^4 = 16\) is

Question and options

Answer and explanation

Practice for these exams

Related question papers

Related exam syllabi

More solved explanations in Arithmetic