If $c^{2} = a^{2} + b^{2}$ solve for $b$ and find the value of $b$ , if $a = 8$ and $c = 17$ .

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Solution

The given quadratic equation is $c^{2} = a^{2} + b^{2}$ .

Substitute $a = 8$ and $c = 17$ in the equation $c^{2} = a^{2} + b^{2}$ as follows:

$c^{2} = a^{2} + b^{2} \Rightarrow 17^{2} = 8^{2} + b^{2} \Rightarrow 289 = 64 + b^{2} \Rightarrow b^{2} = 289 - 64 \Rightarrow b^{2} = 225 \Rightarrow b = \sqrt{225} \Rightarrow b = \pm 15$

Hence, $b = \pm 15$ .

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