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Question-164315




Question Number 164315 by ajfour last updated on 16/Jan/22
Commented by ajfour last updated on 16/Jan/22
If the blue area is   c   units, find p.
$${If}\:{the}\:{blue}\:{area}\:{is}\:\:\:{c}\:\:\:{units},\:{find}\:{p}. \\ $$
Commented by cortano1 last updated on 16/Jan/22
 (1) c = (1/2)×(p^2 −2)(2(√(p^2 −1)))    c = (p^2 −1−1)(√(p^2 −1)) ; (√(p^2 −1)) = y    c=(y^2 −1)y     c= y^3 −y     y^3 −y−c = 0
$$\:\left(\mathrm{1}\right)\:{c}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\left({p}^{\mathrm{2}} −\mathrm{2}\right)\left(\mathrm{2}\sqrt{{p}^{\mathrm{2}} −\mathrm{1}}\right) \\ $$$$\:\:{c}\:=\:\left({p}^{\mathrm{2}} −\mathrm{1}−\mathrm{1}\right)\sqrt{{p}^{\mathrm{2}} −\mathrm{1}}\:;\:\sqrt{{p}^{\mathrm{2}} −\mathrm{1}}\:=\:{y} \\ $$$$\:\:{c}=\left({y}^{\mathrm{2}} −\mathrm{1}\right){y}\: \\ $$$$\:\:{c}=\:{y}^{\mathrm{3}} −{y}\: \\ $$$$\:\:{y}^{\mathrm{3}} −{y}−{c}\:=\:\mathrm{0}\: \\ $$$$\:\: \\ $$$$\: \\ $$
Commented by ajfour last updated on 16/Jan/22
Thanks sir.
$${Thanks}\:{sir}. \\ $$

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