Question

If 4^a2 + b^2 = 40 and ab = 6, find the value of 2a + b.​

Answer 1

Step-by-step explanation:

4a² + b² = 40

(2a)² + (b)² + 2(2a)(b) = 40 + 4ab

( 2a + b )² = 40 + 4(6) = 40+24 = 64

2a + b = 8

Answer 2

$\large{\underline{\underline{\mathfrak{Answer :}}}}$

2a + b = 8

$\rule{200}{0.5}$

$\underline{\underline{\mathfrak{Step-By-Step-Explanation :}}}$

Given :

• $\sf{4a^2 + b^2 = 40}$
• ab = 6

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To Find :

• We have to find value of $\sf{2a + b}$

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Solution :

$\sf{\implies 4a^2 + b^2 = 40} \\ \\ \sf{\implies (2a)^2 + b^2 = 40} \\ \\ \bf{Adding \: 4ab \: both \: sides} \\ \\ \sf{\implies (2a)^2 + b^2 + 4ab = 40 + 4ab} \\ \\ \large{\boxed{\sf{(x + y)^2 = x^2 + y^2 + 2xy}}}$

Where,

• x = 2a
• y = b

$\sf{\implies (2a + b)^2 = 40 + 4(6)} \\ \\ \sf{\implies (2a + b)^2 = 40 + 24} \\ \\ \sf{\implies (2a + b)^2 = 64} \\ \\ \sf{\implies (2a + b) = \sqrt{64}} \\ \\ \sf{\implies 2a + b = (\sqrt{8})^2} \\ \\ \sf{\implies 2a + b = 8} \\ \\ \large{\boxed{\sf{2a + b = 8}}}$