Question 61

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

Given, $$4a^2 + b^2 = 20$$ and $$ab = 4$$

$$=$$> $$4a^2+b^2+4ab-4ab=20$$

$$=$$> $$\left(2a\right)^2+b^2+2.2a.b-4ab=20$$

$$=$$> $$\left(2a+b\right)^2-4ab=20$$

$$=$$> $$\left(2a+b\right)^2-4\left(4\right)=20$$

$$=$$> $$\left(2a+b\right)^2-16=20$$

$$=$$> $$\left(2a+b\right)^2=20+16$$

$$=$$> $$\left(2a+b\right)^2=36$$

$$=$$> $$2a+b=6$$

Hence, the correct answer is Option C

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