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if-x-gt-4-5-x-z-find-x-z-




Question Number 140346 by mathsuji last updated on 06/May/21
if, x>4 ; 5!∙x!=z! ; find: x+z=?
$${if},\:{x}>\mathrm{4}\:;\:\mathrm{5}!\centerdot{x}!={z}!\:;\:{find}:\:{x}+{z}=? \\ $$
Answered by hknkrc46 last updated on 06/May/21
5! = ((z!)/(x!)) ⇒  { ((x = 5! − 1 ⇒ z = 120)),((x + z = 119 + 120 = 239)) :}
$$\mathrm{5}!\:=\:\frac{\boldsymbol{{z}}!}{\boldsymbol{{x}}!}\:\Rightarrow\:\begin{cases}{\boldsymbol{{x}}\:=\:\mathrm{5}!\:−\:\mathrm{1}\:\Rightarrow\:\boldsymbol{{z}}\:=\:\mathrm{120}}\\{\boldsymbol{{x}}\:+\:\boldsymbol{{z}}\:=\:\mathrm{119}\:+\:\mathrm{120}\:=\:\mathrm{239}}\end{cases} \\ $$
Commented by mathsuji last updated on 07/May/21
thankyou sir cool
$${thankyou}\:{sir}\:{cool} \\ $$
Answered by mr W last updated on 06/May/21
5!=120=4×5×6=2×3×4×5  x!×120=z! ⇒x=119, z=120  x!×4×5×6=z! ⇒x=3, z=6  x!×2×3×4×5=z! ⇒x=1, z=5  for x>4 there is only one solution:  x=119,z=120
$$\mathrm{5}!=\mathrm{120}=\mathrm{4}×\mathrm{5}×\mathrm{6}=\mathrm{2}×\mathrm{3}×\mathrm{4}×\mathrm{5} \\ $$$${x}!×\mathrm{120}={z}!\:\Rightarrow{x}=\mathrm{119},\:{z}=\mathrm{120} \\ $$$${x}!×\mathrm{4}×\mathrm{5}×\mathrm{6}={z}!\:\Rightarrow{x}=\mathrm{3},\:{z}=\mathrm{6} \\ $$$${x}!×\mathrm{2}×\mathrm{3}×\mathrm{4}×\mathrm{5}={z}!\:\Rightarrow{x}=\mathrm{1},\:{z}=\mathrm{5} \\ $$$${for}\:{x}>\mathrm{4}\:{there}\:{is}\:{only}\:{one}\:{solution}: \\ $$$${x}=\mathrm{119},{z}=\mathrm{120} \\ $$
Commented by mathsuji last updated on 07/May/21
thakyou sir cool
$${thakyou}\:{sir}\:{cool} \\ $$

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