Question Number 4176 by Yozzii last updated on 31/Dec/15
Commented by Yozzii last updated on 31/Dec/15
$${If}\:{it}'{s}\:{hard}\:{to}\:{read},\:{the}\:{info} \\ $$$${reads}\:{x}\geqslant{b}>\mathrm{0}. \\ $$
Commented by prakash jain last updated on 31/Dec/15
![c=a(√x)−(√(x−b)) c+(√(x−b))=a(√x) a^2 x=c^2 +2c(√(x−b))+x−b (a^2 −1)x−(c^2 −b)=2c(√(x−b)) (a^2 −1)^2 x^2 +(c^2 −b)^2 −2(c^2 −b)(a^2 −1)x=4c^2 (x−b) (a^2 −1)^2 −2[(c^2 −b)(a^2 −1)−2c^2 ]x+(c^2 −b)^2 +4c^2 b=0 need to check Δ](Q4187.png)
$${c}={a}\sqrt{{x}}−\sqrt{{x}−{b}} \\ $$$${c}+\sqrt{{x}−{b}}={a}\sqrt{{x}} \\ $$$${a}^{\mathrm{2}} {x}={c}^{\mathrm{2}} +\mathrm{2}{c}\sqrt{{x}−{b}}+{x}−{b} \\ $$$$\left({a}^{\mathrm{2}} −\mathrm{1}\right){x}−\left({c}^{\mathrm{2}} −{b}\right)=\mathrm{2}{c}\sqrt{{x}−{b}} \\ $$$$\left({a}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} {x}^{\mathrm{2}} +\left({c}^{\mathrm{2}} −{b}\right)^{\mathrm{2}} −\mathrm{2}\left({c}^{\mathrm{2}} −{b}\right)\left({a}^{\mathrm{2}} −\mathrm{1}\right){x}=\mathrm{4}{c}^{\mathrm{2}} \left({x}−{b}\right) \\ $$$$\left({a}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2}\left[\left({c}^{\mathrm{2}} −{b}\right)\left({a}^{\mathrm{2}} −\mathrm{1}\right)−\mathrm{2}{c}^{\mathrm{2}} \right]{x}+\left({c}^{\mathrm{2}} −{b}\right)^{\mathrm{2}} +\mathrm{4}{c}^{\mathrm{2}} {b}=\mathrm{0} \\ $$$$\mathrm{need}\:\mathrm{to}\:\mathrm{check}\:\Delta \\ $$