Class 9 Exam > Class 9 Questions > 1. If x = , prove that (x3 + ) – 5 (...
Start Learning for Free
1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.?
Most Upvoted Answer
1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.?
1. **Given equation:**
Let's start by writing down the equation we need to prove:
\( (x^3 + \frac{1}{x}) - 5(x^2 + \frac{1}{x}) + (x + \frac{1}{x}) = 0 \)
2. **Substitute the given value of x:**
We are given that \( x = \frac{1}{2} \), so let's substitute this value into the equation:
\( (\frac{1}{2}^3 + \frac{1}{\frac{1}{2}}) - 5(\frac{1}{2}^2 + \frac{1}{\frac{1}{2}}) + (\frac{1}{2} + \frac{1}{\frac{1}{2}}) \)
3. **Simplify the equation:**
Now, simplify each term in the equation using the given value of x:
\( (\frac{1}{8} + 2) - 5(\frac{1}{4} + 2) + (\frac{1}{2} + 2) \)
\( (\frac{1}{8} + 2) - 5(\frac{1}{4} + 2) + (\frac{1}{2} + 2) \)
\( (\frac{17}{8}) - 5(\frac{9}{4}) + (\frac{5}{2}) \)
4. **Further simplification:**
Now, simplify the equation further:
\( (\frac{17}{8}) - (\frac{45}{4}) + (\frac{5}{2}) \)
\( \frac{17}{8} - \frac{45}{4} + \frac{10}{4} \)
\( \frac{17}{8} - \frac{35}{4} \)
\( \frac{17}{8} - \frac{70}{8} \)
\( \frac{-53}{8} \)
5. **Conclusion:**
After simplifying the given equation with the value of x, we end up with \( \frac{-53}{8} \), which is not equal to 0. Therefore, the given equation is not true for \( x = \frac{1}{2} \).
Let's start by writing down the equation we need to prove:
\( (x^3 + \frac{1}{x}) - 5(x^2 + \frac{1}{x}) + (x + \frac{1}{x}) = 0 \)
2. **Substitute the given value of x:**
We are given that \( x = \frac{1}{2} \), so let's substitute this value into the equation:
\( (\frac{1}{2}^3 + \frac{1}{\frac{1}{2}}) - 5(\frac{1}{2}^2 + \frac{1}{\frac{1}{2}}) + (\frac{1}{2} + \frac{1}{\frac{1}{2}}) \)
3. **Simplify the equation:**
Now, simplify each term in the equation using the given value of x:
\( (\frac{1}{8} + 2) - 5(\frac{1}{4} + 2) + (\frac{1}{2} + 2) \)
\( (\frac{1}{8} + 2) - 5(\frac{1}{4} + 2) + (\frac{1}{2} + 2) \)
\( (\frac{17}{8}) - 5(\frac{9}{4}) + (\frac{5}{2}) \)
4. **Further simplification:**
Now, simplify the equation further:
\( (\frac{17}{8}) - (\frac{45}{4}) + (\frac{5}{2}) \)
\( \frac{17}{8} - \frac{45}{4} + \frac{10}{4} \)
\( \frac{17}{8} - \frac{35}{4} \)
\( \frac{17}{8} - \frac{70}{8} \)
\( \frac{-53}{8} \)
5. **Conclusion:**
After simplifying the given equation with the value of x, we end up with \( \frac{-53}{8} \), which is not equal to 0. Therefore, the given equation is not true for \( x = \frac{1}{2} \).
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.?
Question Description
1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.?.
1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.?.
Solutions for 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? defined & explained in the simplest way possible. Besides giving the explanation of
1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.?, a detailed solution for 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? has been provided alongside types of 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? theory, EduRev gives you an
ample number of questions to practice 1. If x = , prove that (x3 + ) – 5 (x2 + ) + (x + ) = 0.? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup