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

Question Number 140346 by mathsuji last updated on 06/May/21

i f, x > 4; 5! \cdot x! = z!; f i n d : x + z = ?

Answered by hknkrc46 last updated on 06/May/21

5! = \frac{z!}{x!} \Rightarrow {\begin{cases} x = 5! - 1 \Rightarrow z = 120 \\ x + z = 119 + 120 = 239 \end{cases}

Commented by mathsuji last updated on 07/May/21

t h a n k y o u s i r c o o l

Answered by mr W last updated on 06/May/21

5! = 120 = 4 \times 5 \times 6 = 2 \times 3 \times 4 \times 5

x! \times 120 = z! \Rightarrow x = 119, z = 120

x! \times 4 \times 5 \times 6 = z! \Rightarrow x = 3, z = 6

x! \times 2 \times 3 \times 4 \times 5 = z! \Rightarrow x = 1, z = 5

f o r x > 4 t h e r e i s o n l y o n e s o l u t i o n :

x = 119, z = 120

Commented by mathsuji last updated on 07/May/21

t h a k y o u s i r c o o l