If a+b+ c= 1,( a *a)+ (b*b) + (c*c) = 9 and find (a*a*a) + (b*b* b) + (c* c*c) =1 Find (1/a)+(1/b) + (1/c)
Anjana , 6 Years ago
Grade 10
Algebra> If a+b+ c= 1,( a *a)+ (b*b) + (c*c) = 9 a...
1 Answers
Adarsh Bajpai
Last Activity: 6 Years ago
Given:a+b+c=1
a^2+b^2+c^2=9
a^3+b^3+c^3=1
Now as we all know
(a+b+c)^2=a^2+b^2+c^2+2 (ab+bc+ca)
now putting the values
(1)^2=(9)+2 (ab+bc+ca)
1-9=2 (ab+bc+ca)
-8=2 (ab+bc+ca)
therefore, -4=(ab+bc+ac) …......... [1]
now, a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)
Again putting values
1-3abc=(1){9-(ab+bc+ac)}
1-3abc=9-(-4)
1-3abc=9+4
1-3abc=13
1-13=3abc
-12=3abc
therefore, abc=-4
Now,1/a+1/b+1/c=bc+ac+ab/abc
= -4/ -4
=1
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