Question

If (3+x) : (5+x) : (8+x) then find the Value of x

Answer 1

Answer:

Given: 3x,5x+1,8x−1 are in AP.

We know if a,b,c are in A.P. then b−a=b−c or 2b=a+c

∴2(5x+1)=3x+8x−1

∴10x+2=11x−1

∴11x−10x=2+1

∴x=3

Answer 2

Given,

$\[\left( {3 + x} \right):\left( {5 + x} \right):\left( {8 + x} \right)\]$

Solution,

If a, b, c are in $\[a:b:c\]$, then $\[\frac{a}{b} = \frac{b}{c}\]$

$\[\left( {3 + x} \right):\left( {5 + x} \right):\left( {8 + x} \right)\]$

$\[ \Rightarrow \frac{{\left( {3 + x} \right)}}{{\left( {5 + x} \right)}} = \frac{{\left( {5 + x} \right)}}{{\left( {8 + x} \right)}}\]$

Cross multiply,

$\[\begin{array}{l} \Rightarrow \left( {3 + x} \right)\left( {8 + x} \right) = {\left( {5 + x} \right)^2}\\ \Rightarrow 24 + 11x + {x^2} = 25 + {x^2} + 10x\\ \Rightarrow 24 + 11x = 25 + 10x\\ \Rightarrow x = 1\end{array}\]$

Hence the value of x is 1.