4 2 4 + 2 1 1 + 2 1 5 + 2 1 6 + 2 2 1 + 2 2 4 = ?
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.
Good recognition of how to simplify the expression by identifying the binomial expression.
Same method The question was too beautiful
Can you break down the jump from the third to the fourth step please?
Log in to reply
I have added a line. Hope that it helps.
Lets simplify the part inside the radical first:
2 4 + 2 1 1 + 2 1 5 + 2 1 6 + 2 2 1 + 2 2 4
= 2 4 ( 1 + 2 7 + 2 1 1 + 2 1 2 + 2 1 7 + 2 2 0 )
= 2 4 [ 1 + 2 7 + 2 1 1 + 2 1 7 + ( 2 1 2 + 2 2 0 ) ]
= 2 4 [ 1 + 2 7 + 2 1 1 + 2 1 7 + ( 2 6 + 2 1 0 ) 2 − 2 1 7 ]
= 2 4 [ 1 2 + ( 2 6 + 2 1 0 ) 2 + 2 7 + 2 1 1 ]
= 2 4 [ ( 1 + 2 6 + 2 1 0 ) 2 − 2 7 − 2 1 1 + 2 7 + 2 1 1 ]
= 2 4 [ 1 2 + 2 5 + ( 2 × 1 × 2 5 ) ] 2
= 2 4 [ 1 + 2 5 ] 4 = ( 2 × 3 3 ) 4 = 6 6 4
Now, putting it under the radical, we have 6 6 as the final answer.
For 4 2 4 + 2 1 1 + 2 1 5 + 2 1 6 + 2 2 1 + 2 2 4
Here's the steps:
4 2 4 + 2 1 1 + 2 1 5 + 2 1 6 + 2 2 1 + 2 2 4 = 4 1 6 + 2 0 4 8 + 3 2 7 6 8 + 6 5 5 3 6 + 2 0 9 7 1 5 2 + 1 6 7 7 7 2 1 6 = 4 1 8 9 7 4 7 3 6 = 6 6 □
ADIOS!!!
Do that without a calculator in 2 minutes.
Problem Loading...
Note Loading...
Set Loading...
Relevant wiki: Simplifying Expressions with Radicals - Intermediate
X = 4 2 4 + 2 1 1 + 2 1 5 + 2 1 6 + 2 2 1 + 2 2 4 = 2 4 1 + 2 7 + 2 1 1 + 2 1 2 + 2 1 7 + 2 2 0 Assuming the form of ( 1 + x ) 4 ⟹ x 4 = 2 2 0 ⟹ x = 2 5 = 3 2 = 2 4 1 + 4 ( 2 5 ) + ( 2 + 4 ) ( 2 5 ) 2 + 4 ( 2 5 ) 3 + ( 2 5 ) 4 = 2 4 1 + 4 ( 2 5 ) + 6 ( 2 5 ) 2 + 4 ( 2 5 ) 3 + ( 2 5 ) 4 Note that ( 1 + x ) 4 = 1 + 4 x + 6 x 2 + 4 x 3 + x 4 = 2 4 ( 1 + 2 5 ) 4 = 2 ( 1 + 2 5 ) = 2 ( 1 + 3 2 ) = 6 6