Question

how to solve the following quadratic equations
$4 {x}^{2} - 4 {a}^{2} x + {a}^{4} - {b}^{4}$
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Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: solve \: for : value(s) \: of \: x \\ \\ given \: quadratic \: equation \: is \\ 4x {}^{2} - 4a {}^{2} x + a {}^{4} - b {}^{4} = 0 \\ 4x {}^{2} - 2.2a {}^{2} x + a {}^{4} = b {}^{4} \\ (2x) {}^{2} - 2x.2a {}^{2} +( a {}^{2} ) {}^{2} = b {}^{4} \\ (2x - a {}^{2} ) {}^{2} =( b {}^{2} ) {}^{2} \\ \\ taking \: square \: roots \: on \: both \: sides \\ we \: obtain \\ \\ (2x - a {}^{2} ) = ± \: b {}^{2} \\ \\ 2x - a {}^{2} = b {}^{2} \: \: or \: \: 2x - a {}^{2} = -b {}^{2} \\ \\ 2x = a {}^{2} + b {}^{2} \: \: or \: \: 2x = a {}^{2} - b {}^{2} \\ \\ x = \frac{a {}^{2} + b {}^{2} }{2} \: \: or \: \: x = \frac{a {}^{2} - b {}^{2} }{2}$