SSC Exam > SSC Questions > If ‘a’ and ‘b’ are tw...
Start Learning for Free
If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4 – b4) always divisible?
- a)3
- b)6
- c)8
- d)12
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If ‘a’ and ‘b’ are two odd positive integers, ...
We know that, Summation and Subtraction between two odd integers gives an even integer.
Given, a and b are two odd positive integers.
∴ a + b = 2k1 ……(1)
And a – b = 2k2 ........(2)
Where, k1 and k2are two integers.
(1) + (2) ⇒ 2a = 2(k1 + k2) ⇒ a = k1 + k2
(1) - (2) ⇒ 2b = 2(k1 - k2) ⇒ b = k1 - k2
∴ a2 + b2
= (k1 + k2)2 + (k1 - k2)2
= k12 + k22 + 2k1k2 + k12 + k22 - 2k1k2
= 2(k12 + k22) ………..(3)
Given expression is,
a4 – b4
= (a2 – b2)(a2 + b2)
= (a + b) (a - b)(a2 + b2)
Putting values from (1), (2) and (3)
= 2k1 × 2k2 × 2(k12 + k22)
= 8× k1 × k2 × (k12 + k22)
∴ a4 – b4 = 8× k1 × k2 × (k12 + k22) is always divisible by 8.
Given, a and b are two odd positive integers.
∴ a + b = 2k1 ……(1)
And a – b = 2k2 ........(2)
Where, k1 and k2are two integers.
(1) + (2) ⇒ 2a = 2(k1 + k2) ⇒ a = k1 + k2
(1) - (2) ⇒ 2b = 2(k1 - k2) ⇒ b = k1 - k2
∴ a2 + b2
= (k1 + k2)2 + (k1 - k2)2
= k12 + k22 + 2k1k2 + k12 + k22 - 2k1k2
= 2(k12 + k22) ………..(3)
Given expression is,
a4 – b4
= (a2 – b2)(a2 + b2)
= (a + b) (a - b)(a2 + b2)
Putting values from (1), (2) and (3)
= 2k1 × 2k2 × 2(k12 + k22)
= 8× k1 × k2 × (k12 + k22)
∴ a4 – b4 = 8× k1 × k2 × (k12 + k22) is always divisible by 8.
Most Upvoted Answer
If ‘a’ and ‘b’ are two odd positive integers, ...
You could have any superpower, what would it be and why?
|
Explore Courses for SSC exam
|
|
Similar SSC Doubts
If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?
Question Description
If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?.
If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?.
Solutions for If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
Download more important topics, notes, lectures and mock test series for SSC Exam by signing up for free.
Here you can find the meaning of If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If ‘a’ and ‘b’ are two odd positive integers, by which of the following is (a4– b4) always divisible?a)3b)6c)8d)12Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice SSC tests.
|
|
Explore Courses for SSC exam
|
|
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