given real numbers a,b,c,d1
prove ((a^2)/(c-1))+((b^2)/(d-1))+((c^2)/(e-1))+((d^2)/(a-1))+((e^2)/(b-1)) =20

Question

given real numbers a,b,c,d>1
prove ((a^2)/(c-1))+((b^2)/(d-1))+((c^2)/(e-1))+((d^2)/(a-1))+((e^2)/(b-1)) >=20

anonymous · Answer

$$\frac{ a^2 }{ c-1 } +\frac{b^2}{d-1}+\frac{c^2}{e-1}+\frac{d^2}{a-1}+\frac{e^2}{b-1}\ge20$$

kc_kennylau · Answer

you mean integers

anonymous · Answer

no all real numbers including integers

anonymous · Answer

help guys

anonymous · Answer

help guys

anonymous · Answer

do it for two variables using gradient, you get the minimum of the sum to be 8 and achieved at a=2, b=2
$$

\frac{a^2}{b-1}+\frac{b^2}{a-1}\geq 8
$$
for a, b>1

anonymous · Answer

The general case is messy. Maybe someone else can find an easier method,
What is your background in Math?

anonymous · Answer

i am just 11th standard student

anonymous · Answer

and what is this gradient thing?

anonymous · Answer

OK, so there must be a must be a method not using Calculus. I will do some more work.