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For what real values of $c$ is $x^2 - 8x - 4x + c + x^2 - 20x + x^2$ the square of a binomial?

 May 19, 2024
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Combine like terms

2x^2 - 32x + c

 

binomial square expansion says that (a+b)^2 = a^2 + 2ab + b^2

so a = sqrt2 * x

2ab = 2 * sqrt2 * x * sqrt(c)

-32x = 2 * sqrt2 * x * sqrt(c)

-16 = sqrt(2c)

256 = 2c

c = 128

 May 19, 2024

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