1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Hatshy [7]
3 years ago
13

If a+b+c =0 show that a³+b³+c³= 3abc

Mathematics
1 answer:
slega [8]3 years ago
7 0

Answer:

Step-by-step explanation:

a+b+c=0, a+b=-c,a+c=-b, b+c=-a

(a+b+c)^3=(a+b+c)^2*(a+b+c)=(a^2+b^2+c^2+2ab+2ac+2bc)*(a+b+c)=

a^3+ab^2+ac^2+2a^2b+2a^2c+2abc+a^2b+b^3+bc^2+2ab^2+2abc+2b^2c+a^2c+b^2c+c^3+2abc+2ac^2+2bc^2=a^3+b^3+c^3+3a^2b+3a^2c+3ac^2+3ab^2+3bc^2+3b^2c+6abc=

a^3+b^3+c^3+3a^2*(b+c)+3c^2(a+b)+3b^2(a+c)+6abc=

a^3+b^3+c^3+3a^2*(-a)+3c^2*(-c)+3b^2*(-b)+6abc=

a^3+b^3+c^3-3a^3-3c^3-3b^3+6abc=

6abc-2a^3-2b^3-2c^3=2(3abc-a^3-b^3-c^3)=

2*[3abc-(a^3+b^3+c^3)]=0

so 3abc-(a^3+b^3+c^3)=0

so a^3+b^3+c^3=3abc

You might be interested in
Identify the common external tangent
laiz [17]
A line that is tangent to each of the two coplanar circles
3 0
3 years ago
Read 2 more answers
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!
devlian [24]
I think it’s the third one and the last two. I’m sorry if it’s wrong
7 0
3 years ago
Pls awnser thank you maybe
Zanzabum

Answer:

Step-by-step explanation:

..

6 0
3 years ago
Read 2 more answers
For example of 100 students the median is 90
jenyasd209 [6]

Answer:

How is that possible

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Find the measure of each angle indicated 37° 50° ?​
8_murik_8 [283]

Answer:

<u>93°</u>

Step-by-step explanation:

According to angle sum property, all the internal angles of a triangle add up to 180 degrees.

=> 37 + 50 + ? = 180

=> ? = 180 - 87

=> ? = <u>93°</u>

5 0
2 years ago
Other questions:
  • 4x(7x+5) what is the answer
    13·2 answers
  • |2 1/3 x+0.3|=3.5 <br> |2 1/3 x-0.3|=3.5
    7·2 answers
  • Prove that :-<br><br> Cos3A-cosA/sin3A-sinA+cos2A-cos4A/sin4A-sin2A=sinA/cos2Acos3A
    15·1 answer
  • Molly's friend, Xavier, has 11/8 cups of strawberries. He needs 3/4 cup of strawberries to make a batch of tarts. How many batch
    9·1 answer
  • What does percent mean? Per<br> (Spell the word or write the number)
    8·2 answers
  • Find the value of x.
    10·1 answer
  • Matt took a taxi from his home to the airport. The taxi driver charged an initial fee of $6.75 plus $2.20 per mile. The total fa
    8·2 answers
  • Graph y=x+4 <br> Plz use a graph and show me
    9·2 answers
  • Y = -2x + 5 &amp; y = x - 1<br> Use the Equal Values Method to solve for x and y
    15·1 answer
  • Help me please I am still confused
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!