Equations

Algebra Level 1

If:

{ a i + b i = i a 3 + b 3 = i 6 \begin{cases} ai+bi=i \\ { a }^{ 3 }+{ b }^{ 3 }={ i }^{ 6 } \end{cases}

Find a + b a+b


The answer is 1.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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.

2 solutions

Sharky Kesa
Jun 7, 2014

The second equation is redundant.

a i + b i = i ai + bi = i

i ( a + b ) = i i(a + b) = i

a + b = 1 a + b = 1

Ta dah!

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Got it just by looking at it.

Aman Jaiswal - 7 years ago

The second equation is not redundant, but must be satisfied. The solutions are a = 1/2 + (1/2)sqrt(5/3)I and b = 1/2 - (1/2)sqrt(5/3)I. Ed Gray

Edwin Gray - 2 years, 10 months ago

Log in to reply

It is indeed redundant as the question asks to determine a + b a+b , not determine the actual values of a a and b b .

Sharky Kesa - 2 years, 10 months ago
Shubham Pasari
Aug 20, 2014

Too easy!!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...