Question

cho a +b+c =0; a^2 + b^2 +c^2 = 1. Tính a^4 +b^4 +c^4

 

Answer 1

a^4 + b^4 + c^4 = (a^2 + b^2 + c^2)^2 - 2((ab)^2+(bc)^2+(ca)^2) = 1 - 2((ab)^2+(bc)^2+(ca)^2) (*) 
Do a+b+c = 0 => (a+b+c)^2 = 0 => a^2 + b^2 + c^2 = -2(ab + bc + ca) 
=> (a^2+b^2+c^2)^2 = 4(ab+bc+ca)^2 = 4.((ab)^2+(bc)^2+(ca)^2+2abc(a+b+c)) 
= 4.((ab)^2+(bc)^2+(ca)^2) 
=> a^4 + b^4 + c^4 = 2.((ab)^2+(bc)^2+(ca)^2) 
Thay lại vào (*) ta có a^4 + b^4 + c^4 = 1/2 

Answer 2

(a+b+c)²=a²+b²+c²+2ac+2bc+2ab

=>0²=1+2(ac+bc+ab)

=>ac+bc+ab=-1/2

=>(ac+bc+ab)²=a²b²+b²c²+a²c²+2a²bc+2b²ac+2c²ab

(ac+bc+ab)²=a²b²+b²c²+a²c²+2abc(a+b+c)

=>(-1/2)²=a²b²+b²c²+a²c²+2abc.0

=>a²b²+b²c²+a²c²=1/4

(a²+b²+c²)²=a⁴+b⁴+c⁴+2a²b²+2b²c²+2a²c²

(a²+b²+c²)²=a⁴+b⁴+c⁴+2(a²b²+b²c²+a²c²)

1²=a⁴+b⁴+c⁴+2.1/4

1=a⁴+b⁴+c⁴.1/2

a⁴+b⁴+c⁴=1-1/2=1/2

 

Answer 3

t.i.c.k mik mik t.i.c.k lại

Answer 4

= 1/2 nhé

Mình tính rồi !