If $b = \sqrt{4 a c - d}$ $b=sqrt(4ac-d)$ Then What is $a^{2} - 2 b^{2} + c^{2}$ $a^2-2b^2+c^2$ ?

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Answer 1 · 2018-05-20T14:57:30

$a^{2} - 8 a c + 2 d + c^{2}$ $a^2-8ac+2d+c^2$

$b = \sqrt{4 a c - d}$ $b=sqrt(4ac-d)$
$a^{2} - 2 b^{2} + c^{2}$ $a^2-2b^2+c^2$

substitute $b$ $b$ into the second equation:

$a^{2} - 2 {(\sqrt{4 a c - d})}^{2} + c^{2}$ $a^2-2(sqrt(4ac-d))^2+c^2$

$a^{2} - 2 (4 a c - d) + c^{2}$ $a^2-2(4ac-d)+c^2$

$a^{2} - 8 a c + 2 d + c^{2}$ $a^2-8ac+2d+c^2$