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If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴? using identities solve my question?
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If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴?...
To solve for a and b given the equations a + b = 24 and a - b = 16, we can use algebraic methods and identities to find the required values.
Step 1: Solve for a and b
- Add the two equations:
- (a + b) + (a - b) = 24 + 16
- 2a = 40
- a = 20
- Substitute a back into the first equation:
- 20 + b = 24
- b = 4
Step 2: Calculate a² + b²
- Use the identity a² + b² = (a + b)² - 2ab:
- a + b = 24, therefore (a + b)² = 24² = 576
- Now we need to find ab.
Step 3: Calculate ab
- Use the identity ab = ((a + b)² - (a - b)²) / 4:
- (a + b)² = 576
- (a - b)² = 16² = 256
- ab = (576 - 256) / 4 = 320 / 4 = 80
Step 4: Calculate a² + b² (continued)
- Now substitute ab back into the identity:
- a² + b² = 576 - 2(80) = 576 - 160 = 416
Step 5: Calculate a⁴ + b⁴
- Use the identity a⁴ + b⁴ = (a² + b²)² - 2(ab)²:
- a² + b² = 416, so (a² + b²)² = 416² = 173056
- ab = 80, so (ab)² = 80² = 6400
- a⁴ + b⁴ = 173056 - 2(6400) = 173056 - 12800 = 160256
Final Results
- a² + b² = 416
- ab = 80
- a⁴ + b⁴ = 160256
Step 1: Solve for a and b
- Add the two equations:
- (a + b) + (a - b) = 24 + 16
- 2a = 40
- a = 20
- Substitute a back into the first equation:
- 20 + b = 24
- b = 4
Step 2: Calculate a² + b²
- Use the identity a² + b² = (a + b)² - 2ab:
- a + b = 24, therefore (a + b)² = 24² = 576
- Now we need to find ab.
Step 3: Calculate ab
- Use the identity ab = ((a + b)² - (a - b)²) / 4:
- (a + b)² = 576
- (a - b)² = 16² = 256
- ab = (576 - 256) / 4 = 320 / 4 = 80
Step 4: Calculate a² + b² (continued)
- Now substitute ab back into the identity:
- a² + b² = 576 - 2(80) = 576 - 160 = 416
Step 5: Calculate a⁴ + b⁴
- Use the identity a⁴ + b⁴ = (a² + b²)² - 2(ab)²:
- a² + b² = 416, so (a² + b²)² = 416² = 173056
- ab = 80, so (ab)² = 80² = 6400
- a⁴ + b⁴ = 173056 - 2(6400) = 173056 - 12800 = 160256
Final Results
- a² + b² = 416
- ab = 80
- a⁴ + b⁴ = 160256
Community Answer
If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴?...
Answer it please
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If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴? using identities solve my question? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴? using identities solve my question? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴? using identities solve my question?.
If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴? using identities solve my question? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴? using identities solve my question? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a+ b = 24 and a- b =16 find the value of a) a²+ b² b) ab c) a⁴ +b⁴? using identities solve my question?.
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