Trinomial trauma

Algebra Level 3

a + b + c = 1 a + b + c = 1
a 2 + b 2 + c 2 = 2 a^2 + b^2 + c^2 = 2
a 3 + b 3 + c 3 − 3 a b c = x a^3 + b^3 + c^3 - 3abc = x

Find 2 x 2x .


The answer is 5.

View wiki
Stephen Hannarn by Stephen Hannarn , 111, Thailand

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Anik Mandal
Sep 9, 2014

( a + b + c ) = 1 (a+b+c)=1

( a + b + c ) 2 = 1 (a+b+c)^{2}=1

a 2 + b 2 + c 2 + 2 ( a b + b c + c a ) = 1 a^{2}+b^{2}+c^{2}+2(ab+bc+ca)=1

2 + 2 ( a b + b c + c a ) = 1 2+2(ab+bc+ca)=1

a b + b c + c a = − 1 2 ab+bc+ca=\frac{-1}{2}

We know,

a 3 + b 3 + c 3 − 3 a b c a^{3}+b^{3}+c^{3}-3abc

= ( a + b + c ) ( a 2 + b 2 + c 2 − a b − b c − c a ) (a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)

= ( 1 ) . ( 2 + 1 2 ) (1).(2+\frac{1}{2})

= 5 2 \frac{5}{2}

Therefore, x = 5 2 x=\frac{5}{2} and 2 x = 5 2x=5

5 Helpful 0 Interesting 0 Brilliant 0 Confused

I've got a full set on these kind of problems you might like, bit tougher concept ... Bashing Unavailable

Aditya Raut - 6 years, 9 months ago

Log in to reply

Thanks! @Aditya Raut I will surely have a try on them...... By the way are you on gmail or Fb or something like that?

Anik Mandal - 6 years, 9 months ago

Log in to reply

I am first of all a human on all of them, later thing ... my name there is "Aditya Raut" , and even more info, my pro pic is the same everywhere, "drop of color"

Aditya Raut - 6 years, 9 months ago

Exactly..!!

Tripurna Chary - 6 years, 9 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...