Question

If 1/x+2, 1/x+3, 1/x+5 are in AP then x=

Answer 1

Answer:

1

Step-by-step explanation:

Since these are in AP, these must satisfy the indentities of AP(2b = a + c, a, b, c are consecutive AP terms).

So, here,

=> 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)(x+5)

=> 2(x+2)(x+5) = (2x+7)(x+3)

=> 2(x²+7x+10) = 2x²+13x+21

=> 2x² + 14x + 20 = 2x² + 13x + 21

=> 14x - 13x = 21 - 20

=> x = 1