Madhya Pradesh Police Exam Model Paper 6

Question : 73 of 101

Marks: +1, -0

If a and b are two positive real numbers such that

4a^2 + b^2 = 20

and

ab = 4

, then the value of

2a + b

is:

Solution:

Tips & Tricks
Given :

4a^2 + b^2 = 20

ab = 4

To find :

2a + b

Formula used :

a^2 + b^2 = (a + b)^2 - 2ab

Solution :

4a^2 + b2 = 20

⇒ (2a)^2 + b^2 = 20

⇒ (2a + b)^2 - 2 × 2a × b = 20

⇒ (2a + b)^2 - 4 × 4 = 20

⇒ (2a + b)^2 - 16 = 20

⇒ (2a + b)^2 = 20 + 16

⇒ (2a + b)^2 = 36

⇒ 2a + b = √36

⇒ 2a + b = 6

∴ the value of 2a + b is 6.

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