JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(a+b+c=1, a b+b c+c a=2\) and \(a b c=3\), then the value of \(a^{4}+b^{4}+c^{4}\) is equal to \(....\)
- A \(15\)
- B \(13\)
- C \(17\)
- D \(21\)
Answer & Solution
Correct Answer
(B) \(13\)
Step-by-step Solution
Detailed explanation
\({a^{2}+b^{2}+c^{2}=(a+b+c)^{2}-2 \Sigma a b=-3}\) \({(a b+b c+c a)^{2}=\Sigma(a b)^{2}+2 a b c \sum a}\) \({\Rightarrow \Sigma(a b)^{2}=-2}\) \({a^{4}+b^{4}+c^{4}=\left(a^{2}+b^{2}+c^{2}\right)^{2}-2 \Sigma(a b)^{2}}\) \({\quad=9-2(-2)=13}\)
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