Given:
The numbers 1/(x+2), 1/(x+3), and 1/(x+5) are in Arithmetic progression.
To Find:
The value of x.
Solution:
The given problem can be solved using the concepts of Arithmetic Progression.
1. Let t1, t2, t3 be three consecutive terms of an A.P then,
=> t2 - t1 = t3 - t2 ( As the three terms are in Arithmetic progression )
2. Use the above property for the given problem,
=>
=> x² + 2x - 3 = 0
=> x² + 3x - x - 3 = 0
=> x(x+3) -1(x+3) = 0
=> (x-1)(x+3) = 0
=> x = 1 (OR) x = -3
3. For x = -3 the value 1/(x+3) is not defined ( Since the denominator is 0 )
=> The value of x is 1.
=> 1/3, 1/4, and 1/6 are the terms.
Therefore, the value of x is 1.
Answer:THIS IS THE ANSWER
Step-by-step explanation:
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Answers & Comments
Given:
The numbers 1/(x+2), 1/(x+3), and 1/(x+5) are in Arithmetic progression.
To Find:
The value of x.
Solution:
The given problem can be solved using the concepts of Arithmetic Progression.
1. Let t1, t2, t3 be three consecutive terms of an A.P then,
=> t2 - t1 = t3 - t2 ( As the three terms are in Arithmetic progression )
2. Use the above property for the given problem,
=>
=>
=>
=>
=>
=>
=> x² + 2x - 3 = 0
=> x² + 3x - x - 3 = 0
=> x(x+3) -1(x+3) = 0
=> (x-1)(x+3) = 0
=> x = 1 (OR) x = -3
3. For x = -3 the value 1/(x+3) is not defined ( Since the denominator is 0 )
=> The value of x is 1.
=> 1/3, 1/4, and 1/6 are the terms.
Therefore, the value of x is 1.
Verified answer
Answer:THIS IS THE ANSWER
Step-by-step explanation: