Question

CHECK THE ATTACHMENT ​

Answer 1

Solution:

Given That:

$\rm \longrightarrow \dfrac{23}{7} =a + \dfrac{1}{b + \frac{1}{c} }$

We have to find out the value of a + b + c. It can be written as:

$\rm \longrightarrow a +\dfrac{1}{b + \frac{1}{c} } =3 \dfrac{2}{7}$

$\rm \longrightarrow a +\dfrac{1}{b + \frac{1}{c} } =3 + \dfrac{2}{7}$

Can be written as:

$\rm \longrightarrow a +\dfrac{1}{b + \frac{1}{c} } =3 + \dfrac{1}{ \frac{7}{2} }$

$\rm \longrightarrow a +\dfrac{1}{b + \frac{1}{c} } =3 + \dfrac{1}{ 3\frac{1}{2} }$

$\rm \longrightarrow a +\dfrac{1}{b + \frac{1}{c} } =3 + \dfrac{1}{ 3 + \frac{1}{2} }$

Comparing both sides, we get:

$\rm \longrightarrow \begin{cases} \rm a = 3 \\ \rm b = 3 \\ \rm c = 2\end{cases}$

Therefore:

$\rm \longrightarrow a + b + c = 3 + 3 + 2$

$\rm \longrightarrow a + b + c =8$

★ Which is our required answer.

Answer:

• a + b + c = 8