If a , b ∈ R satisfy the equation a 2 + 4 b 2 - 4 = 0 , then the minimum value of 2 a + 3 b will be

Question

If a , b ∈ R satisfy the equation a 2 + 4 b 2 - 4 = 0 , then the minimum value of 2 a + 3 b will be, - 4, - 5, - 6, - 10

MARKS App · Accepted Answer

Given equation is a 2 4 + b 2 = 1 Putting a = 2 cos ⁡ θ , b = sin ⁡ θ , we get, 2 a + 3 b = 2 2 cos ⁡ θ + 3 sin ⁡ θ = 4 cos θ + 3 sin θ ⇒ Minimum value = - 4 2 + 3 2 = - 5

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