Aptitude - Surds and Indices - Discussion

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"You cannot shake hands with a clenched fist."

- Indira Gandhi

1 + 1 + 1 = ?

1 + x^{(b - a)} + x^{(c - a)} 1 + x^{(a - b)} + x^{(c - b)} 1 + x^{(b - c)} + x^{(a - c)}

[A].	0	[B].	1
[C].	x^{a - b - c}	[D].	None of these

Answer: Option B

Explanation:

Given Exp. =

1 + 1 + 1

1 + x^b + x^c

x^a x^a

1 + x^a + x^c

x^b x^b

1 + x^b + x^a

x^c x^c

= x^a + x^b + x^c

(x^a + x^b + x^c) (x^a + x^b + x^c) (x^a + x^b + x^c)

= (x^a + x^b + x^c)

(x^a + x^b + x^c)

= 1.

Raju said: (Sat, Feb 5, 2011 10:00:45 AM)

I didn't understand the second line.

Kunaman said: (Sat, May 7, 2011 10:02:22 AM)

@raju We took the lcm of the denominator of the expression 1+x^b/x^a...

Vasundhara said: (Sat, Oct 8, 2011 04:26:45 PM)

It is the shortcut and easiest way to solve this problem.

Arshad said: (Fri, May 4, 2012 03:37:14 PM)

I did not understood second step from last. Can you please explain in detail(only last two steps) How do you consider x^a+x^b+x^c in numerator ?(x^a+x^b+x^c/x^a+x^b+x^c)

Sagar said: (Sun, Jun 10, 2012 12:56:30 PM)

The second step is derived from first step by multiplying numerator & denominator of each of the 3 components with x^a, x^b & x^c respectively.

Anagha said: (Sat, May 25, 2013 02:33:27 PM)

How do you solve the second step? Really confusing, please do it the long way so we can understand.