How is this supposed to work?
Evaluate this expression without using a calculator. ( 2 3 0 4 9 5 7 2 0 3 4 8 − 1 2 3 0 4 8 7 1 0 9 3 8 4 + 2 ) ( 1 2 3 0 4 8 7 1 0 9 3 8 4 − 2 3 0 4 9 5 7 2 0 3 4 8 + 1 ) − ( 1 + 2 3 0 4 9 5 7 2 0 3 4 8 − 1 2 3 0 4 8 7 1 0 9 3 8 4 ) ( 1 + 1 2 3 0 4 8 7 1 0 9 3 8 4 − 2 3 0 4 9 5 7 2 0 3 4 8 − 1 ) .
The answer is 2.
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3 solutions
I would suggest to insert c = a − b to it.
- The easiest way is you let
- a=230495720348
- b=1230487109384
- c=230495720348 - 1230487109384
- then now you can use the variables to compute for its value
- (2-c)(c+1) -(1-c)(c)
- 2
Since there are a lot of repetition, express the numbers like so:
x = 1
y = 2 3 0 4 9 5 7 2 0 3 4 8
z = 1 2 3 0 4 8 7 1 0 9 3 8 4
With these variables, you can rewrite the expression like so:
( y − z + x + 1 ) ( z − y + x ) − ( x + y − z ) ( x + z − y − 1 )
Multiplying this expression out yields 2 x and since x = 1 , the answer is 2 .
Moderator note:
That's a great use of algebra!
Cannot see the question.The submission box is blocking it.
Let:
a = 2 3 0 4 9 5 7 2 0 3 4 8
b = 1 2 3 0 4 8 7 1 0 9 3 8 4
( a − b + 1 ) ( b − a + 1 ) − ( 1 + a − b ) ( 1 + b − a − 1 )
( a − b + 1 ) ( b − a + 1 ) − ( 1 + a − b ) ( b − a )
Expand them and we get:
2 a b − a 2 − b 2 − a + b + 2 − ( 2 a b − a 2 − b 2 + b − a )
= 2 a b − a 2 − b 2 − a + b + 2 − 2 a b + a 2 + b 2 − b + a )
= 2