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Question Number 123143 by aurpeyz last updated on 23/Nov/20

w r i t e {a x}^{2} + b x + c a s a s u m o r d i f f e r e n c e

o f t w o s q u a r e s

Commented by mr W last updated on 23/Nov/20

= {(\sqrt{a} x)}^{2} + 2 (\frac{b}{2 \sqrt{a}} \times \sqrt{a}) x + {(\frac{b}{2 \sqrt{a}})}^{2} + c - \frac{b^{2}}{4 a}

= {(\sqrt{a} x + \frac{b}{2 \sqrt{a}})}^{2} - {(\sqrt{\frac{b^{2}}{4 a} - c})}^{2} f o r c < \frac{b^{2}}{4 a}

= {(\sqrt{a} x + \frac{b}{2 \sqrt{a}})}^{2} + {(\sqrt{c - \frac{b^{2}}{4 a}})}^{2} f o r c ⩾ \frac{b^{2}}{4 a}

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