Question

Solve 36/11= 3+1/(x+1/(y+1/z))

Answer 1

1.05=4x i
$\\ \\ {2}^{2}$

Answer 2

If $\frac{36}{11}= 3 + \frac{1}{x + \frac{1}{y+\frac{1}{z} } }$ , where x, y, and z are natural numbers, then what is

(x+ y+ z) equal to?

x+ y+ z = 6

Given:

$\frac{36}{11}= 3 + \frac{1}{x + \frac{1}{y+\frac{1}{z} } }$

To Find:

The value of x+ y+ z

Solution:

$\frac{36}{11}= 3 + \frac{1}{x + \frac{1}{y+\frac{1}{z} } }$

$\frac{36}{11}- 3 = \frac{1}{x+\frac{1}{y+\frac{1}{z} } }$

$\frac{36-33}{11} = \frac{1}{x+\frac{1}{y+\frac{1}{z} } } \\\\\frac{3}{11} = \frac{1}{x+\frac{1}{y+\frac{1}{z} } }$

$\frac{1}{x+\frac{1}{y+\frac{1}{z} } } = \frac{1}{\frac{11}{3} } \\\\ \frac{1}{x+\frac{1}{y+\frac{1}{z} } } = \frac{1}{3+\frac{2}{3} }\\\\ \frac{1}{x+\frac{1}{y+\frac{1}{z} } } = \frac{1}{3+\frac{1}{\frac{3}{2} } } \\\\ \frac{1}{x+\frac{1}{y+\frac{1}{z} } } = \frac{1}{3+\frac{1}{1+\frac{1}{ 2} } }$

On comparing LHS and RHS

x= 3, y = 1 and z=2.

⇒x+y+z = 3+1+2 = 6

∴x+ y+ z = 6

#SPJ3

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