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# [Smart Math] Algebra Problem 2

Here’s and example of a SMART MATH problem for ALGEBRA. ### Problem

If $x-y=3$ and $x^{3}-y^{3}=189$; $x+y$ =?

1. 5
2. 7
3. 9
4. 11
5. 13

### The Usual Method

You are suppose to remember the formula $(x-y)^{3}=x^{3}-y^{3}-3xy(x-y)$ $\therefore$ $(x-y)^{3}$ = $3^{3}$ = 27

Also, $x^{3}-y^{3}$ = 189 $\therefore$27 = 189 – 3 $xy$(3) $\therefore$27 = 189 – 9 $xy$ $\therefore$ $xy$ = $\frac{189-27}{9}$ = $\frac{162}{9}$ = 18
Now, $(x+y)^{2}=(x-y)^{2}+4xy$ = $3^{2}$ + 4 (18)
= 9 + 72
= 81

(Ans: 2)

Estimated Time to arrive at the answer = 90 seconds

### Using Technique

Simply write the values of ‘x’ and ‘y’ such that x – y = 3 and x + y = the values in the options as shown below:
5 => 4, 1
7 => 5, 2
9 => 6, 3
11 => 7, 4
13 => 8, 5

Now, start cubing the values of ‘x’ and ‘y’ and find the option for which the difference is = 189. $4^{3}-1^{3}=64-1=63\ne 189$ $5^{3}-2^{3}=125-8=117\ne 189$ $6^{3}-3^{3}=216-27=189$
This should be the answer. There is no need to solve further as there cannot be more than one answer. $\therefore$ $x+y$ = 9

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds
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