IF A+B+C=5 AND AB+BC+CA=10 THEN PROVE THAT A³+B³+C³ -3ABC =-25

Asked by vrishti TOKAS | 20th May, 2015, 08:05: PM

Expert Answer:

$G i v e n space t h a t space A plus B plus C equals 5 space a n d space A B plus B C plus C A equals 10 W e space n e e d space t o space p r o v e space t h a t space A cubed plus B cubed plus C cubed minus 3 A B C equals negative 25 C o n s i d e r space t h e space i d e n t i t y A cubed plus B cubed plus C cubed minus 3 A B C equals open parentheses A plus B plus C close parentheses open parentheses A squared plus B squared plus C squared minus A B minus B C minus C A close parentheses T h u s comma space s u b s t i t u t i n g space t h e space v a l u e s space A plus B plus C equals 5 space a n d space A B plus B C plus C A equals 1 comma space w e space h a v e comma A cubed plus B cubed plus C cubed minus 3 A B C equals 5 cross times open square brackets A squared plus B squared plus C squared minus A B minus B C minus C A close square brackets rightwards double arrow A cubed plus B cubed plus C cubed minus 3 A B C equals 5 cross times open square brackets open parentheses A squared plus B squared plus C squared close parentheses minus open parentheses A B plus B C plus C A close parentheses close square brackets rightwards double arrow A cubed plus B cubed plus C cubed minus 3 A B C equals 5 cross times open square brackets open parentheses A squared plus B squared plus C squared close parentheses minus 10 close square brackets... left parenthesis 1 right parenthesis W e space n e e d space t o space f i n d space t h e space v a l u e space o f space A squared plus B squared plus C squared colon A squared plus B squared plus C squared equals open parentheses A plus B plus C close parentheses squared minus 2 open parentheses A B plus B C plus C A close parentheses rightwards double arrow A squared plus B squared plus C squared equals 5 squared minus 2 cross times 10 rightwards double arrow A squared plus B squared plus C squared equals 25 minus 20 rightwards double arrow A squared plus B squared plus C squared equals 5 T h e r e f o r e comma space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma A cubed plus B cubed plus C cubed minus 3 A B C equals 5 cross times open square brackets 5 minus 10 close square brackets rightwards double arrow A cubed plus B cubed plus C cubed minus 3 A B C equals 5 cross times open square brackets negative 5 close square brackets rightwards double arrow A cubed plus B cubed plus C cubed minus 3 A B C equals negative 25$

Answered by Vimala Ramamurthy | 21st May, 2015, 11:04: AM

Related Videos

This video explains the definition of polynomial and related terms, identif...

Discuss various algebraic operations on Polynomials. Learn the statement a...

This video explains the factorization of polynomials using Factor Theorem a...

Understand the Algebraic identities for quadratic Polynomials. Apply the i...

Listing of algebraic identities for cubic Polynomials and simplify the comp...

Ask Doubt