ab-c-let-a-p-b-q-0-c-aq-bp-pq-0-q-bp-c-p-a-say-4-2-8-4-3-2-6-8-1-1-0-0-And-if-q-b-p-ab-c-2b-0-And-if-p-q-c-p-a-c-p-bp-c-p-2-a-c-b-p-c-1-a-0-2p-a-c-b

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Question Number 140908 by ajfour last updated on 14/May/21

ab=c let (a−p)(b−q)=0 ⇒ c−(aq+bp)+pq=0 q=((bp−c)/(p−a)) say 4×2=8 (4−3)(2−((6−8)/(−1)))=1×0=0 And if q=b p=((ab−c)/(2b))=0 And if p+q=c (p−a)(c−p)=bp−c p^2 −(a+c−b)p+c(1−a)=0 2p=(a+c−b)±(√((a+c−b)^2 −4c(1−a))) ________________________

$$\:\:{ab}={c} \\ $$$${let}\:\:\:\left({a}−{p}\right)\left({b}−{q}\right)=\mathrm{0} \\ $$$$\Rightarrow\:\:{c}−\left({aq}+{bp}\right)+{pq}=\mathrm{0} \\ $$$${q}=\frac{{bp}−{c}}{{p}−{a}} \\ $$$${say}\:\:\:\mathrm{4}×\mathrm{2}=\mathrm{8} \\ $$$$\:\:\:\:\:\left(\mathrm{4}−\mathrm{3}\right)\left(\mathrm{2}−\frac{\mathrm{6}−\mathrm{8}}{−\mathrm{1}}\right)=\mathrm{1}×\mathrm{0}=\mathrm{0} \\ $$$${And}\:\:{if}\:\:{q}={b} \\ $$$$\:\:{p}=\frac{{ab}−{c}}{\mathrm{2}{b}}=\mathrm{0} \\ $$$${And}\:{if}\:{p}+{q}={c} \\ $$$$\left({p}−{a}\right)\left({c}−{p}\right)={bp}−{c} \\ $$$${p}^{\mathrm{2}} −\left({a}+{c}−{b}\right){p}+{c}\left(\mathrm{1}−{a}\right)=\mathrm{0} \\ $$$$\mathrm{2}{p}=\left({a}+{c}−{b}\right)\pm\sqrt{\left({a}+{c}−{b}\right)^{\mathrm{2}} −\mathrm{4}{c}\left(\mathrm{1}−{a}\right)} \\ $$$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ $$

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ab-c-let-a-p-b-q-0-c-aq-bp-pq-0-q-bp-c-p-a-say-4-2-8-4-3-2-6-8-1-1-0-0-And-if-q-b-p-ab-c-2b-0-And-if-p-q-c-p-a-c-p-bp-c-p-2-a-c-b-p-c-1-a-0-2p-a-c-b

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