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If a + b + c = 1 a 2 + b 2 + c 2 = 2 a 3 + b 3 + c 3 = 3 Then Find, a 4 + b 4 + c 4 and a 5 + b 5 +c 5 ?

If 
a + b + c = 1
a2 + b2 + c2 = 2
a3 + b3 + c3 = 3
Then Find,
a4 + b4 + c4 and a5 + b5 +c?
 

Grade:9

1 Answers

Arun
25763 Points
3 years ago

If a+b+c=1,a2+b2+c2=2,a3+b3+c3=3 then find the value of a4+b4+c4=?

we know

2(ab+bc+ca)=(a+b+c)2(a2+b2+c2)

2(ab+bc+ca)=122=1

ab+bc+ca=12

given

a3+b3+c3=3

a3+b3+c33abc+3abc=3

(a+b+c)(a2+b2+c2abbcca)+3abc=3

(a+b+c)(a2+b2+c2(ab+bc+ca)+3abc=3

(1×(2(12)+3abc))=3

(2+12)+3abc=3

3abc=352=12

abc=16

Now

(a2b2+b2c2+c2a2)

=(ab+bc+ca)22ab2c2bc2a2ca2b

=(ab+bc+ca)22abc(b+c+a)

=(12)22×16×1=1413=112

Now

a4+b4+c4

=(a2+b2+c2)22(a2b2+b2c2+c2a2)

=222×(112)

=4+16=416

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