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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