1.

If a + 2b = 10 and 2ab = 9, then |a - 2b| is equal to:1. 42. 83. 24. 6

Answer» Correct Answer - Option 2 : 8

Given:

a + 2b = 10 and 2ab = 9

Formula used:

(a + b)2 = a2 + b2 + 2ab

(a - b)2 = a2 +b2 – 2ab

Calculation:

On squaring both sides of given equation we get,

(a + 2b)2 = (10)2

⇒ (a2 + 4b2 +4ab) = 100

⇒ a2 + 4b2 + 18 = 100  

⇒ a2 + 4b2 = 82

Now,

(a – 2b)2 = a2 +4b2 -4ab

Substituting values of a2 + 4b2 and 4ab from above

We get,

(a – 2b)2 = 82 – 18

⇒ (a – 2b)2 = 64

⇒ (a – 2b) = ±8

⇒ |a – 2b| = 8

∴ The value of |a – 2b| is 8


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