0

Guest

Courses New

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)

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)

Grade:10

1 Answers

Adarsh Bajpai
36 Points
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

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More