SSC Exam > SSC Questions > If (a2+ b2) = 40 and (a + b) = 8, find the va...
Start Learning for Free
If (a2 + b2) = 40 and (a + b) = 8, find the value of (a3 + b3).
- a)128
- b)152
- c)224
- d)344
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)15...
Short trick:
If we put a = 6 and b = 2, both the given conditions are satisfied.
⇒ (a3 + b3) = 63 + 23 = 224
If we put a = 6 and b = 2, both the given conditions are satisfied.
⇒ (a3 + b3) = 63 + 23 = 224
Detailed solution:
∵ (a + b)2 = (a2 + b2) + 2ab
Substituting values,
⇒ (8)2 = 40 + 2ab
⇒ ab = (64 - 40)/2 = 24/2 = 12
∵ (a + b)2 = (a2 + b2) + 2ab
Substituting values,
⇒ (8)2 = 40 + 2ab
⇒ ab = (64 - 40)/2 = 24/2 = 12
Now,
∵ (a3 + b3) = (a + b)3 - 3ab(a + b)
∴ (a3 + b3) = (8)3 - 3(12)(8) = 512 - 288 = 224
∵ (a3 + b3) = (a + b)3 - 3ab(a + b)
∴ (a3 + b3) = (8)3 - 3(12)(8) = 512 - 288 = 224
Most Upvoted Answer
If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)15...
Given Information:
(a^2 - b^2) = 40
(a - b) = 8
Calculating (a + b):
Using the identity a^2 - b^2 = (a + b)(a - b), we can find:
(a + b) = (a^2 - b^2) / (a - b)
(a + b) = 40 / 8
(a + b) = 5
Finding (a^3 - b^3):
Using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2), we can calculate:
(a^3 - b^3) = (a - b)((a + b)^2 + ab)
(a^3 - b^3) = 8(5^2 + ab)
(a^3 - b^3) = 8(25 + ab)
Substitute (a + b) value:
From the calculation above, we know that (a + b) = 5. Substitute this into the equation:
(a^3 - b^3) = 8(25 + 5b)
(a^3 - b^3) = 8(25 + 5(8))
(a^3 - b^3) = 8(25 + 40)
(a^3 - b^3) = 8(65)
(a^3 - b^3) = 520
Therefore, the value of (a^3 - b^3) is 520, which is not listed in the options provided.
|
Explore Courses for SSC exam
|
|
Similar SSC Doubts
If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct answer is option 'C'. Can you explain this answer?
Question Description
If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct 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 (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct 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 (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct answer is option 'C'. Can you explain this answer?.
If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct 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 (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct 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 (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct answer is option 'C'. Can you explain this answer?.
Solutions for If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct 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 (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If (a2+ b2) = 40 and (a + b) = 8, find the value of (a3+ b3).a)128b)152c)224d)344Correct 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