Question

1/x+2 ,1/x+3 ,1/x+5 are in A.P find x ,How the LCM taken in this problem

Answer 1

Answer:

x = 1

For solution , please refer to the attachment .

Note:

★ AP (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are same .

★ If a , b , c are in AP then 2b = a + c and vice versa .

★ The general term of an AP is given by ;

T(n) = a + (n-1)d , where a is the first term and d is the common difference of the AP .

Answer 2

a1=1/x+2

a2=1/x+3

a3=1/x+5

common difference=a2 - a1=a3 - a2

2(a2)=a3+a1

2(1/x+3)=1/x+2 + 1/x+5

2/x+3=(x+5+x+2)/(x+2)(x+5)

2/x+3=(2x+7)/x^2+7x+10

2x^2+14x+20=2x^2+13x+21

14x - 13x=20 - 21

x=1