Mistakes gave rise to another problem!

Algebra Level 3

In mathematics, If you do the following: $-(a-b)=-a-b$ , then It's a big mistake.

How many ordered pairs such that $-10\leq a,b \leq10$ exist such that the mistake given above is true?

Take $a,b$ as integers.

The answer is 21.

2 solutions

Mehul Arora
Jun 24, 2015

$-(a-b)=-a-b$

$-a+b=-a-b$

$-2b=0,b=0$

Now, The mistake above will be true only if $b=0$

Now, When $b=0$ We have $21$ choices for $a$

Therefore, 21 pairs $a,b$ exist so that the 'mistake' stated above is true.

Good question

Aditya Kumar - 5 years, 11 months ago

Thanks! :D Glad you liked it :)

Mehul Arora - 5 years, 11 months ago

Keep creating more and more problems. That'll actually help u

Aditya Kumar - 5 years, 11 months ago

@Aditya Kumar – Ohh Yeah? :P Sure!

Mehul Arora - 5 years, 11 months ago

@Mehul Arora – Yes , keep posting . :)

Nihar Mahajan - 5 years, 11 months ago

@Nihar Mahajan – Yeah, I will :D

Mehul Arora - 5 years, 11 months ago

Good solution

Debmalya Mitra - 5 years, 11 months ago

Thank you! :)

Mehul Arora - 5 years, 11 months ago

In that manner you also counted (0,0) which I intentionally excluded and gave the answer 20... so (a,b) do not require to be distinct?

Milind Chakraborty - 5 years, 10 months ago

U r right as he included (0,0) for both a and b it cant be 21 bu.t 20

Gaurav Dhingra - 5 years, 8 months ago

Israel Bablozi
Oct 29, 2015

Simplifying the expression, the result will be $b=0$ . Therefore, it means that for any integer a within the range, b must be 0. Then, there are 21 cases for that to occur.

Mistakes gave rise to another problem!

The answer is 21.

2 solutions

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