If (3 + 2\(\sqrt {5}\))2 = 29 + K\(\sqrt

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If (3 + 2\(\sqrt {5}\))² = 29 + K\(\sqrt {5}\)

Find value of K²

Options:

144

Correct Answer:

144

Explanation:

Formula → (a + b)² = a² + b² + 2ab

Given, (3 + 2\(\sqrt {5}\))² = 29 + K\(\sqrt {5}\)

⇒ 9 + 20 + 12\(\sqrt {5}\) = 29 + K\(\sqrt {5}\)

29 + 12\(\sqrt {5}\) = 29 + K\(\sqrt {5}\) [compare coefficients]

K = 12

K² = 144