Question

solve the quadratic equation 4x2-4a2x+(a4-b4)=0

Answer 1

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4x^2 - 4a^2x + (a^4 - b^4) = 0

4x^2 - (2a^2 - 2b^2) x - (2a^2 + 2b^2) x + (a^4 - b^4) = 0

2x[2x - (a^2 - b^2)] - (a^2 + b^2)[2x - (a^2 - b^2)] = 0

[2x - (a^2 - b^2)][2x - (a^2 + b^2)] = 0

.: factors are, x = a^2 + b^2 / 2 , a^2 - b^2 / 2.

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