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1-x-1-y-1-z-16-37-then-faind-volve-of-x-y-z-




Question Number 166398 by mathlove last updated on 19/Feb/22
(1/(x+(1/(y+(1/z)))))=((16)/(37))  then faind volve of    x+y+z=?
$$\frac{\mathrm{1}}{{x}+\frac{\mathrm{1}}{{y}+\frac{\mathrm{1}}{{z}}}}=\frac{\mathrm{16}}{\mathrm{37}} \\ $$$${then}\:{faind}\:{volve}\:{of}\:\:\:\:{x}+{y}+{z}=? \\ $$
Answered by floor(10²Eta[1]) last updated on 19/Feb/22
((16)/(37))=(1/((37)/(16)))=(1/(2+(5/(16))))=(1/(2+(1/((16)/5))))=(1/(2+(1/(3+(1/5)))))  x+y+z=10
$$\frac{\mathrm{16}}{\mathrm{37}}=\frac{\mathrm{1}}{\frac{\mathrm{37}}{\mathrm{16}}}=\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{5}}{\mathrm{16}}}=\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\frac{\mathrm{16}}{\mathrm{5}}}}=\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{5}}}} \\ $$$$\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{10} \\ $$

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