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Question-151973




Question Number 151973 by ajfour last updated on 24/Aug/21
Commented by ajfour last updated on 24/Aug/21
OB=OC=(√(OA))  ; OM=1  yellow area=1/4 , then find  OB=OC =x   or  OA=x^2 .
$${OB}={OC}=\sqrt{{OA}}\:\:;\:{OM}=\mathrm{1} \\ $$$${yellow}\:{area}=\mathrm{1}/\mathrm{4}\:,\:{then}\:{find} \\ $$$${OB}={OC}\:={x}\:\:\:{or}\:\:{OA}={x}^{\mathrm{2}} . \\ $$
Answered by ajfour last updated on 24/Aug/21
Commented by ajfour last updated on 25/Aug/21
(s+(√(s^2 −a^2 )))(a+b)=2c+2(√(s^2 −1))  (a+b)^2 =s^2 −1+(1+(√(b^2 +s^2 −a^2 )))^2   (s^2 −1)(s^2 −2)^2 =c^2   To someone who cares, for this  Find s from above 3 eqs.
$$\left({s}+\sqrt{{s}^{\mathrm{2}} −{a}^{\mathrm{2}} }\right)\left({a}+{b}\right)=\mathrm{2}{c}+\mathrm{2}\sqrt{{s}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\left({a}+{b}\right)^{\mathrm{2}} ={s}^{\mathrm{2}} −\mathrm{1}+\left(\mathrm{1}+\sqrt{{b}^{\mathrm{2}} +{s}^{\mathrm{2}} −{a}^{\mathrm{2}} }\right)^{\mathrm{2}} \\ $$$$\left({s}^{\mathrm{2}} −\mathrm{1}\right)\left({s}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{2}} ={c}^{\mathrm{2}} \\ $$$${To}\:{someone}\:{who}\:{cares},\:{for}\:{this} \\ $$$${Find}\:{s}\:{from}\:{above}\:\mathrm{3}\:{eqs}. \\ $$

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