Question

if a4+b4=14a2+b2, then let us show that log a2+b2=log a +log b +2log 2​

Answer 1

Answer:Given a+b+c=0 and (a2+b2+c2)=1, Now (a2+b2+c2)2=12=1

(a4+b4+c4)+2(a2b2+b2c2+c2a2)=1.................(1)

and from (a+b+c)2=0,

we get 1+2(ab+bc+ca)=0⇒(ab+bc+ca)=−12

again squaring both side , we get (ab+bc+ca)2=14

(a2b2+b2c2+c2a2)+2abc(a+b+c)=14⇒(a2b2+b2c2+c2a2)=14

So put in eqn.... (1) , we get

(a4+b4+c4)+2⋅14=1⇒(a4+b4+c4)=12

Step-by-step explanation: