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If a + b + c = 0 and a^(2) + b^(2) + c^(...

If `a + b + c = 0 and a^(2) + b^(2) + c^(2) = 4,` them find the value of `a^(4) + b^(4) +c^(4)`.

Text Solution

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The correct Answer is:
`a^(4) + b^(4) +c^(4) = 8`
`(a + b + c)^(2) = 0`
`rArr a^(2) + b^(2) + c^(2) + 2(ab + bc + ca) = 0`
`rArr ab + bc + ca = -2`
On squaring, we get
`a^(2) b^(2) + b^(2)c^(2)+ c^(2)a^(2)+ 2(ab^(2)c + 2a^(2) bc + 2bac^(2) = 4`
`rArr a^(2) b^(2) + b^(2)c^(2)+ c^(2)a^(2)+ 2abc (a + b + c) = 4`
`rArr a^(2) b^(2) + b^(2)c^(2)+ c^(2)a^(2) = 4`
Now `a^(2) + b^(2) + c^(2) = 4`
On squaring, we get
`a^(4)+ b^(4)+ c^(4)+2(a^(2) b^(2) + b^(2)c^(2)+ c^(2)a^(2) = 16`
`rArr a^(4)+ b^(4)+ c^(4)= 8`
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