Write the value of - for which x2-4 x- is a perfect square-

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Solving a Quadratic Equation by Factorization Method

Write the val...

Question

Write the value of λ for which x² + 4x + λ is a perfect square.

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Solution

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λ

x^{2} + 4 x + λ = 0

λ

4 x + 3 y + λ = 0

x^{2} + y^{2} - 6 x + 4 y - 12 = 0

4 y - 3 x + λ = 0

x^{2} + y^{2} - 4 x - 8 y - 5 = 0

λ

λ

x^{2}

x^{2} {(\sqrt{x} + \frac{λ}{x^{2}})}^{10}

720

λ

x^{2} + (3 - λ) x + 2 = λ

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