Basics & LogarithmseasyJEE Main 2021Free

Basics & Logarithms — JEE Maths practice question (JEE Main 2021)

JEE Maths question with a full step-by-step solution.

Question
If a+b+c=1a+b+c=1, ab+bc+ca=2ab+bc+ca=2 and abc=3abc=3, then the value of a4+b4+c4a^{4}+b^{4}+c^{4} is equal to
Solution
Answer: 13
Step 1: Use the identity:
a2+b2+c2=(a+b+c)2−2(ab+bc+ca)=1−2(2)=−3a^{2}+b^{2}+c^{2}=(a+b+c)^{2}-2(ab+bc+ca)=1-2(2)=-3
 Step 2:
(ab+bc+ca)2=∑(ab)2+2∑ab2c=4(ab+bc+ca)^{2}=\sum(ab)^{2}+2\sum ab^{2}c=4
∑(ab)2=(ab+bc+ca)2−2abc(a+b+c)=4−2(3)(1)=−2\sum(ab)^{2}=(ab+bc+ca)^{2}-2abc(a+b+c)=4-2(3)(1)=-2
 Step 3:
a4+b4+c4=(a2+b2+c2)2−2[(ab)2+(bc)2+(ca)2]a^{4}+b^{4}+c^{4}=(a^{2}+b^{2}+c^{2})^{2}-2[(ab)^{2}+(bc)^{2}+(ca)^{2}]
=(−3)2−2(−2)=9+4=13=(-3)^{2}-2(-2)=9+4=13
 Answer: 1313
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