Question : if $a-b=3$ and $a^3-b^3=117$, then $|a+b|$ is equal to:
Option 1: 3
Option 2: 5
Option 3: 7
Option 4: 9
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Correct Answer: 7
Solution :
Given:
a – b = 3
a
3
– b
3
= 117
We know,
a
3
– b
3
= (a – b)
3
+ 3ab(a – b)
⇒ 117 = 27 + 3ab(3)
⇒ 9ab = 117 – 27
⇒ 9ab = 90
So, ab = 10
Now, (a + b)
2
= (a – b)
2
+ 4ab = 9 + 40 = 49
∴ |a + b| = 7
Hence, the correct answer is 7.
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