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Question Number 184251 by Shrinava last updated on 04/Jan/23

If x (√y) = 2904 Find: y=?

$$\mathrm{If}\:\:\:\mathrm{x}\:\sqrt{\mathrm{y}}\:=\:\mathrm{2904} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{y}=? \\ $$

Answered by SEKRET last updated on 04/Jan/23

x∙(√y) = 2^3 ∙3∙11^2 { ((x=2)),(((√y) =2^2 ∙11^2 ∙3)) :} { ((x=2^2 )),(((√y) =2∙3∙11^2 )) :} { ((x=2^3 )),(((√y) =3∙11^2 )) :} { ((x=2^2 ∙3∙11^2 )),(((√y) =2)) :} { ((x=2∙3∙11^2 )),(((√y) =2^2 )) :} { ((x=3∙11^2 )),(((√y) =2^3 )) :} { ((x=3)),(((√y) =2^3 ∙11^2 )) :} { ((x=11)),(((√y) =2^3 ∙11∙3)) :} { ((x=11^2 )),(((√y) =2^3 ∙3)) :} { (( x=2^3 ∙11^2 )),(((√y) =3)) :} { (( x=2^3 ∙11∙3)),(((√y) = 11)) :} { ((x=2^3 ∙3)),(((√(y )) =11^2 )) :} { ((x=1)),(((√y) =2904)) :} { ((x=2904)),(((√y) = 1)) :} { ((x=2∙3)),(((√y) =2^2 ∙11^2 )) :} { ((x=2^2 ∙3)),(((√y) =2∙11^2 )) :} { ((x=2^3 ∙3)),(((√y) =11^2 )) :} { ((x=2^2 ∙11^2 )),(((√y) =2∙3)) :} { ((x=2∙11^(22) )),(((√y) =2^2 ∙3)) :} { ((x=11^2 )),(((√y) =2^3 ∙3)) :} ........ .............

$$\:\:\:\boldsymbol{\mathrm{x}}\centerdot\sqrt{\boldsymbol{\mathrm{y}}}\:=\:\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} \\ $$$$\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{11}^{\mathrm{2}} \centerdot\mathrm{3}}\end{cases}\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{2}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} }\end{cases}\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{3}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} }\end{cases} \\ $$$$\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} \:\:\:\:}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}}\end{cases}\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{2}} \:}\end{cases}\:\:\:\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{3}} }\end{cases} \\ $$$$\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{3}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{11}^{\mathrm{2}} \:}\end{cases}\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{11}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{11}\centerdot\mathrm{3}}\end{cases}\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{11}^{\mathrm{2}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{3}}\end{cases} \\ $$$$\:\begin{cases}{\:\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{11}^{\mathrm{2}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{3}}\end{cases}\:\:\:\:\begin{cases}{\:\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{11}\centerdot\mathrm{3}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\:\mathrm{11}}\end{cases}\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{3}}\\{\sqrt{\boldsymbol{\mathrm{y}}\:}\:=\mathrm{11}^{\mathrm{2}} }\end{cases} \\ $$$$\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{1}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2904}}\end{cases}\:\:\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2904}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\:\mathrm{1}}\end{cases} \\ $$$$\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}\centerdot\mathrm{3}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{11}^{\mathrm{2}} }\end{cases}\:\:\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}\centerdot\mathrm{11}^{\mathrm{2}} }\end{cases}\:\:\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{3}}\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{11}^{\mathrm{2}} }\end{cases} \\ $$$$\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{11}^{\mathrm{2}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}\centerdot\mathrm{3}}\end{cases}\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{2}\centerdot\mathrm{11}^{\mathrm{22}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{3}}\end{cases}\:\:\:\begin{cases}{\boldsymbol{\mathrm{x}}=\mathrm{11}^{\mathrm{2}} }\\{\sqrt{\boldsymbol{\mathrm{y}}}\:=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{3}}\end{cases} \\ $$$$\:........ \\ $$$$............. \\ $$

Answered by SEKRET last updated on 04/Jan/23

(√y) = ((2904)/x) x≠0 y = ((2904^2 )/x^2 )

$$\:\:\:\:\sqrt{\boldsymbol{\mathrm{y}}}\:\:\:=\:\frac{\mathrm{2904}}{\boldsymbol{\mathrm{x}}}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{x}}\neq\mathrm{0} \\ $$$$\:\:\:\:\:\:\boldsymbol{\mathrm{y}}\:=\:\frac{\mathrm{2904}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \\ $$

Answered by mr W last updated on 04/Jan/23

for x,y∈Z, there are 24 solutions. y=(((2^3 ×3×11^2 )/x))^2

$${for}\:{x},{y}\in{Z},\:{there}\:{are}\:\mathrm{24}\:{solutions}. \\ $$$${y}=\left(\frac{\mathrm{2}^{\mathrm{3}} ×\mathrm{3}×\mathrm{11}^{\mathrm{2}} }{{x}}\right)^{\mathrm{2}} \\ $$

Answered by Ml last updated on 04/Jan/23

x=2904 y=1

$$\mathrm{x}=\mathrm{2904} \\ $$$$\mathrm{y}=\mathrm{1} \\ $$

Answered by Rasheed.Sindhi last updated on 04/Jan/23

x(√y) =2^3 ∙3∙11^2 y is perfect square & divisor of 2904 y=1,2^2 ,11^2 ,(2×11)^2 =1,4,121,484

$${x}\sqrt{{y}}\:=\mathrm{2}^{\mathrm{3}} \centerdot\mathrm{3}\centerdot\mathrm{11}^{\mathrm{2}} \\ $$$${y}\:{is}\:{perfect}\:{square}\:\&\:{divisor}\:{of}\:\mathrm{2904} \\ $$$${y}=\mathrm{1},\mathrm{2}^{\mathrm{2}} ,\mathrm{11}^{\mathrm{2}} ,\left(\mathrm{2}×\mathrm{11}\right)^{\mathrm{2}} \\ $$$$\:\:\:=\mathrm{1},\mathrm{4},\mathrm{121},\mathrm{484} \\ $$

Commented by mr W last updated on 04/Jan/23

please recheck sir! i think y must not be divisor of 2904. (√y) is divisor of 2904. since 2904 has 24 divisors, (√y) may have 24 possible values, therefore y may also have 24 possible values, not only 5 values. for example y=2904^2 is also a valid solution.

$${please}\:{recheck}\:{sir}! \\ $$$${i}\:{think}\:{y}\:{must}\:{not}\:{be}\:{divisor}\:{of}\:\mathrm{2904}. \\ $$$$\sqrt{{y}}\:{is}\:{divisor}\:{of}\:\mathrm{2904}.\:{since}\:\mathrm{2904}\:{has} \\ $$$$\mathrm{24}\:{divisors},\:\sqrt{{y}}\:{may}\:{have}\:\mathrm{24}\:{possible} \\ $$$${values},\:{therefore}\:{y}\:{may}\:{also}\:{have} \\ $$$$\mathrm{24}\:{possible}\:{values},\:{not}\:{only}\:\mathrm{5}\:{values}. \\ $$$${for}\:{example}\:{y}=\mathrm{2904}^{\mathrm{2}} \:{is}\:{also}\:{a}\:{valid} \\ $$$${solution}. \\ $$

Commented by Rasheed.Sindhi last updated on 04/Jan/23

You′re right sir! It′s my mistake!

$${You}'{re}\:{right}\:\boldsymbol{{sir}}!\:{It}'{s}\:{my}\:{mistake}! \\ $$

Answered by Frix last updated on 04/Jan/23

x(√y)=2904 (√y)=((2904)/x) y=(((2904)/x))^2 I don′t get all the complicated answers. It′s like a+(b/2)=15 Find: b=? What am I missing?

$${x}\sqrt{{y}}=\mathrm{2904} \\ $$$$\sqrt{{y}}=\frac{\mathrm{2904}}{{x}} \\ $$$${y}=\left(\frac{\mathrm{2904}}{{x}}\right)^{\mathrm{2}} \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{get}\:\mathrm{all}\:\mathrm{the}\:\mathrm{complicated}\:\mathrm{answers}. \\ $$$$\mathrm{It}'\mathrm{s}\:\mathrm{like} \\ $$$${a}+\frac{{b}}{\mathrm{2}}=\mathrm{15} \\ $$$$\mathrm{Find}:\:{b}=? \\ $$$$\mathrm{What}\:\mathrm{am}\:\mathrm{I}\:\mathrm{missing}? \\ $$

Commented by Frix last updated on 04/Jan/23

People don′t answer given questions but instead adding something new to questions before solving them?!?

$$\mathrm{People}\:\mathrm{don}'\mathrm{t}\:\mathrm{answer}\:\mathrm{given}\:\mathrm{questions}\:\mathrm{but} \\ $$$$\mathrm{instead}\:\mathrm{adding}\:\mathrm{something}\:\mathrm{new}\:\mathrm{to}\:\mathrm{questions} \\ $$$$\mathrm{before}\:\mathrm{solving}\:\mathrm{them}?!? \\ $$

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