Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 112208 by Khalmohmmad last updated on 06/Sep/20

Commented by Dwaipayan Shikari last updated on 06/Sep/20

x=9              (from observation)  y=4

$${x}=\mathrm{9} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\left({from}\:{observation}\right) \\ $$$${y}=\mathrm{4} \\ $$$$ \\ $$

Commented by Khalmohmmad last updated on 06/Sep/20

solving method ??

$$\mathrm{solving}\:\mathrm{method}\:?? \\ $$

Commented by Dwaipayan Shikari last updated on 06/Sep/20

x=(7−y)^2   (7−y)^2 =11−(√y)     (y=a^2 )  (7−a^2 )^2 =11−a  a^4 −14a^2 +49=11−a  a^4 −14a^2 +a+38=0  a=2  y=4  x=3^2 =9

$${x}=\left(\mathrm{7}−{y}\right)^{\mathrm{2}} \\ $$$$\left(\mathrm{7}−{y}\right)^{\mathrm{2}} =\mathrm{11}−\sqrt{{y}}\:\:\:\:\:\left({y}={a}^{\mathrm{2}} \right) \\ $$$$\left(\mathrm{7}−{a}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{11}−{a} \\ $$$${a}^{\mathrm{4}} −\mathrm{14}{a}^{\mathrm{2}} +\mathrm{49}=\mathrm{11}−{a} \\ $$$${a}^{\mathrm{4}} −\mathrm{14}{a}^{\mathrm{2}} +{a}+\mathrm{38}=\mathrm{0} \\ $$$${a}=\mathrm{2} \\ $$$${y}=\mathrm{4} \\ $$$${x}=\mathrm{3}^{\mathrm{2}} =\mathrm{9} \\ $$

Answered by bemath last updated on 07/Sep/20

(√x) = p ; (√y) = q   { ((p+q^2 =7)),((p^2 +q=11)) :}⇒ p=7−q^2   ⇒(7−q^2 )^2 +q =11 , q^4 −14q^2 +49+q−11=0  q^4 −14q^2 +q+38=0  factoring   (q−2)(q^3 +2q^2 +4q−19)=0  → { ((q=2→2=(√y) , y=4)),((q^3 +2q^2 +4q−19=0)) :}

$$\sqrt{\mathrm{x}}\:=\:\mathrm{p}\:;\:\sqrt{\mathrm{y}}\:=\:\mathrm{q} \\ $$$$\begin{cases}{\mathrm{p}+\mathrm{q}^{\mathrm{2}} =\mathrm{7}}\\{\mathrm{p}^{\mathrm{2}} +\mathrm{q}=\mathrm{11}}\end{cases}\Rightarrow\:\mathrm{p}=\mathrm{7}−\mathrm{q}^{\mathrm{2}} \\ $$$$\Rightarrow\left(\mathrm{7}−\mathrm{q}^{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{q}\:=\mathrm{11}\:,\:\mathrm{q}^{\mathrm{4}} −\mathrm{14q}^{\mathrm{2}} +\mathrm{49}+\mathrm{q}−\mathrm{11}=\mathrm{0} \\ $$$$\mathrm{q}^{\mathrm{4}} −\mathrm{14q}^{\mathrm{2}} +\mathrm{q}+\mathrm{38}=\mathrm{0} \\ $$$$\mathrm{factoring}\: \\ $$$$\left(\mathrm{q}−\mathrm{2}\right)\left(\mathrm{q}^{\mathrm{3}} +\mathrm{2q}^{\mathrm{2}} +\mathrm{4q}−\mathrm{19}\right)=\mathrm{0} \\ $$$$\rightarrow\begin{cases}{\mathrm{q}=\mathrm{2}\rightarrow\mathrm{2}=\sqrt{\mathrm{y}}\:,\:\mathrm{y}=\mathrm{4}}\\{\mathrm{q}^{\mathrm{3}} +\mathrm{2q}^{\mathrm{2}} +\mathrm{4q}−\mathrm{19}=\mathrm{0}}\end{cases} \\ $$$$ \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com