If a + 2b = 27 and $a^3 + 8b^3 = 5427$,

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If a + 2b = 27 and $a^3 + 8b^3 = 5427$, then find the value of 2ab.

Options:

176

156

172

149

Correct Answer:

176

Explanation:

Given,

a + 2b = 27

a³ + 8b³ = 5427

We know that,

(A + B)³ = A³ + B³ + 3AB(A + B)

= (27)³ = 5427 + 3 × 2ab(27)

= 19683 = 5427 + 81 × 2ab

= 81 × 2ab = 14256

= 2ab = 176