Ta có 

\(a+b+c=0\Rightarrow\left(a+b+c\right)^2=0^2\Rightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)

Mà \(a^2+b^2+c^2=14\)

\(\Rightarrow14+2\left(ab+bc+ca\right)=0\Rightarrow2\left(ab+bc+ca\right)=-14\Rightarrow ab+bc+ca=-7\)

\(\Rightarrow\left(ab+bc+ca\right)^2=\left(-7\right)^2\Rightarrow a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)=49\)

Mà \(a+b+c=0\)

\(\Rightarrow a^2b^2+b^2c^2+c^2a^2=49\)(1)

Ta lại có 

\(a^2+b^2+c^2=14\Rightarrow\left(a^2+b^2+c^2\right)^2=\left(14\right)^2\Rightarrow a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=196\)

\(\Rightarrow a^4+b^4+c^4=196-2\left(a^2b^2+b^2c^2+c^2a^2\right)\)(2)

Thay (1) vào (2) 

\(a^4+b^4+c^4=196-2.49=98\)

nha - Cảm ơn 

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Ta có: a + b + c = 0

=> (a + b + c)² = 0

=> a² + b² + c² + 2(ab + bc + ac) = 0

=> 14 + 2(ab + bc + ac) = 0

=> 2ab + 2bc + 2ac = -14

=> (2ab + 2bc + 2ac)² = 196

=> 4a²b² + 4a²c² + 4b²c² + 8ab²c + 8a²bc + 8abc² = 196

=> 4(a²b² + b²c² + c²a²) + 8abc(b + a + c) = 196

=> 4(a²b² + b²c² + c²a²) = 196

=> 2(a²b² + b²c² + c²a²) = 98

Có: a² + b² + c² = 14

=> (a² + b² + c²)² = 196

=> a⁴ + b⁴ + c⁴ + 2(a²b² + b²c² + a²c²) = 196

Mà 2(a²b² + b²c² + a²c²) = 98

=> a⁴ + b⁴ + c⁴ = 98

Vậy a⁴ + b⁴ + c⁴ = 98

 a+b+c = 0 
<=> (a+b+c)^2 = 0 
<=> a^2 + b^2 + c^2 + 2 ab + 2ac + 2bc = 0 
<=>14 + 2(ab + ac + bc) = 0 
<=> 2(ab + ac + bc) = -14 
<=> ab + ac + bc = -7 
=> (ab + ac + bc)^2 = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 + 2a^2bc + 2 ab^2c + 2abc^2 = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 + 2abc(a + b + c) = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 + 2abc . 0 = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 = 49 

Ta có: a^2 + b^2 + c^2 = 14 
=> (a^2 + b^2 + c^2)^2 = 14^2 
<=> a^4 + b^4 + c^4 + 2a^2b^2 + 2a^2c^2 + 2 b^2c^2 =196 
<=> a^4 + b^4 + c^4 + 2(a^2b^2 + a^2c^2 + b^2c^2) = 196 
<=> a^4 + b^4 + c^4 + 2 . 49 = 196 
<=> a^4 + b^4 + c^4 + 98 = 196 
<=> a^4 + b^4 + c^4 = 98 

 a+b+c = 0 
<=> (a+b+c)^2 = 0 
<=> a^2 + b^2 + c^2 + 2 ab + 2ac + 2bc = 0 
<=>14 + 2(ab + ac + bc) = 0 
<=> 2(ab + ac + bc) = -14 
<=> ab + ac + bc = -7 
=> (ab + ac + bc)^2 = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 + 2a^2bc + 2 ab^2c + 2abc^2 = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 + 2abc(a + b + c) = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 + 2abc . 0 = 49 
<=> a^2b^2 + a^2c^2 + b^2c^2 = 49 

Ta có: a^2 + b^2 + c^2 = 14 
=> (a^2 + b^2 + c^2)^2 = 14^2 
<=> a^4 + b^4 + c^4 + 2a^2b^2 + 2a^2c^2 + 2 b^2c^2 =196 
<=> a^4 + b^4 + c^4 + 2(a^2b^2 + a^2c^2 + b^2c^2) = 196 
<=> a^4 + b^4 + c^4 + 2 . 49 = 196 
<=> a^4 + b^4 + c^4 + 98 = 196 
<=> a^4 + b^4 + c^4 = 98 

98

nhớ bấm đúng cho mình nhé!

xin lỗi bạn có thể trình bày cách làm đc ko /

ta có a+b+c=0

\(\Rightarrow\left(a+b+c\right)^2=0\)

\(a^2+b^2+c^2+2\left(ab+ac+bc\right)=0\)

\(ab+ac+bc=-7\)

\(\left(ab+ac+bc\right)^2=49\)

\(a^2b^2+a^2c^2+b^2c^2+2abc\left(a+b+c\right)=49\)

\(a^2b^2+a^2c^2+b^2c^2=49\left(a+b+c=0\right)\)

\(\left(a^2+b^2+c^2\right)^2=14^2\)

\(a^4+b^4+c^4+2\left(a^2b^2+a^2c^2+b^2c^2\right)=196\)

\(a^4+b^4+c^4=196-98=98\)

a+b+c=0

=>(a+b+c)²=0

=>a²+b²+c²+2(ab+bc+ac)=0

=>2(ab+bc+ac)=-14(do a²+b²+c²=14)

Ta có:a²+b²+c²=14

=>(a²+b²+c²)²=196

=>a⁴+b⁴+c⁴+2(a²b²+b²c²+a²c²)=196(1)

2(ab+bc+ac)=-14

=>(2ab+2bc+2ac)²=196

=>4(a²b²+c²b²+a²c²)+2abc(a+b+c)=196

Do a+b+c=0

=>4(a²b²+c²b²+a²c²)=196 =>2(a²b²+c²b²+a²c²)=98(2)

Từ(1) và (2) =>a⁴+b⁴+c⁴=98

Sai rồi bạn ơi!

a+b+c=0

=>(a+b+c)²=0

=>a²+b²+c²+2(ab+bc+ac)=0

=>2(ab+bc+ac)=-14(do a²+b²+c²=14)

Ta có:a²+b²+c²=14

=>(a²+b²+c²)²=196

=>a⁴+b⁴+c⁴+2(a²b²+b²c²+a²c²)=196(1)

2(ab+bc+ac)=-14

=>(2ab+2bc+2ac)²=196

=>4(a²b²+c²b²+a²c²)+2abc(a+b+c)=196

Do a+b+c=0

=>4(a²b²+c²b²+a²c²)=196 =>2(a²b²+c²b²+a²c²)=98(2)

Từ(1) và (2) =>a⁴+b⁴+c⁴=98

a² + b²  + c²=14

hay(a + b + c)² = 14

a⁴ + b⁴ + c⁴ =(a² + b² + c²).(a² + b² + c²)=(a+b+c)² . (a+b+c)² =14.14=196

k mk nha bạn kb nữa

Từ \(a+b+c=0\Leftrightarrow a^2+b^2+c^2=-2\left(ab+bc+ca\right)\)

\(\Leftrightarrow-7=ab+bc+ca\)\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)=49\)

\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2=49\left(\text{vi` a+b+c=0}\right)\)

Ma tu \(a^2+b^2+c^2=14\)

\(\Leftrightarrow a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=14^2\)

\(\Leftrightarrow a^4+b^4+c^4=14^2-2\cdot49=....\)