Cho các số nguyên a,b,c thỏa mãn : 2014×a^2+b^2+c^2/a^2 = a^2+2014×b^2+c^2/b^2= a^2+b^2+2014×c^2/c^2
Tính giá trị biểu thức : P = 2015×a^2+b^2/c^2+2015×b^2+c^2/a^2+2015×c^2+a^2/b^2
Cho các số nguyên a,b,c thỏa mãn : 2014×a^2+b^2+c^2/a^2 = a^2+2014×b^2+c^2/b^2= a^2+b^2+2014×c^2/c^2
Tính giá trị biểu thức : P = 2015×a^2+b^2/c^2+2015×b^2+c^2/a^2+2015×c^2+a^2/b^2
[Bai_1]
$\dfrac{2014a^2+b^2+c^2}{a^2}=\dfrac{a^2+2014b^2+c^2}{b^2}=\dfrac{2^2+b^2+2014c^2}{c^2}$
$=>2014+\dfrac{b^2+c^2}{a^2}=2014+\dfrac{a^2+c^2}{b^2}=2014+\dfrac{a^2+b^2}{c^2}$
$=>\dfrac{b^2+c^2}{a^2}=\dfrac{a^2+c^2}{b^2}=\dfrac{a^2+b^2}{c^2}$
$=>\dfrac{b^2+c^2+a^2+c^2+a^2+b^2}{a^2+b^2+c^2}=\dfrac{2(a^2+b^2+c^2)}{a^2+b^2+c^2}=2$
$=>\dfrac{b^2}{a^2}+\dfrac{c^2}{a^2}=\dfrac{a^2}{b^2}+\dfrac{c^2}{b^2}=\dfrac{a^2}{c^2}+\dfrac{b^2}{c^2}=2$
$=>\dfrac{b^2}{a^2}+\dfrac{c^2}{a^2}+\dfrac{a^2}{b^2}+\dfrac{c^2}{b^2}+\dfrac{a^2}{c^2}+\dfrac{b^2}{c^2}=6$
$=>\dfrac{b^2}{a^2}+\dfrac{c^2}{a^2}+\dfrac{c^2}{b^2}=3$
[Bai_2]
$P=\dfrac{2015a^2+b^2}{c^2}+\dfrac{2015b^2+c^2}{a^2}+\dfrac{2015c^2+a^2}{b^2}$
$P=2015\bigg(\dfrac{a^2}{c^2}+\dfrac{b^2}{a^2}+\dfrac{c^2}{b^2}\bigg)+\bigg(\dfrac{b^2}{c^2}+\dfrac{c^2}{a^2}+\dfrac{c^2}{b^2}\bigg)$
$P=\bigg(\dfrac{a^2}{c^2}+\dfrac{b^2}{a^2}+\dfrac{c^2}{b^2}\bigg)(2015+1)$
$P=\bigg(\dfrac{a^2}{c^2}+\dfrac{b^2}{a^2}+\dfrac{c^2}{b^2}\bigg).2016$
$P=3.2016=6048$