SSC JE Exam  >  SSC JE Questions  >  What are the roots of a equation (a+b+x)1 = a... Start Learning for Free
What are the roots of a equation (a+b+x)–1 = a–1 + b–1 + x–1 ?
  • a)
    a, b    
  • b)
    -a, b    
  • c)
    a, -b    
  • d)
    -a, -b
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a,...
Free Test
Community Answer
What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a,...
Roots of an Equation

An equation is said to have roots when the values of the variable that satisfy the equation are found. In other words, the roots of an equation are the values of the variable that make the equation true.

Given Equation

The given equation is (a b x)1 = a1 b1 x1. Here, the 1 is an exponent and not a coefficient.

Finding the Roots

To find the roots of the equation (a b x)1 = a1 b1 x1, we can use the rule of exponents which states that if two exponential expressions with the same base are equal, then their exponents must be equal as well. Using this rule, we can write:

a b x = a1 b1 x1

Taking the logarithm of both sides, we get:

log(abx) = log(a1b1x1)

Using the properties of logarithms, we can simplify the equation as:

log(a) + log(b) + log(x) = log(a1) + log(b1) + log(x1)

Now, we can solve for x by isolating it on one side of the equation:

log(x) = log(a1) + log(b1) + log(x1) - log(a) - log(b)

log(x) = log[x1(b1/a)(1/b)]

x = x1(b1/a)(1/b)

Therefore, the roots of the equation (a b x)1 = a1 b1 x1 are:

x = x1(b1/a)(1/b)

And since the exponent 1/b is equivalent to taking the b-th root, we can write the roots as:

x = x1(∛(b1/a))^-b

Hence, the correct option is (D) -a, -b.
Explore Courses for SSC JE exam
What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer?
Question Description
What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer? for SSC JE 2024 is part of SSC JE preparation. The Question and answers have been prepared according to the SSC JE exam syllabus. Information about What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC JE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer?.
Solutions for What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC JE. Download more important topics, notes, lectures and mock test series for SSC JE Exam by signing up for free.
Here you can find the meaning of What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice What are the roots of a equation (a+b+x)1 = a1 + b1 + x1 ?a)a, b b)-a, b c)a, -b d)-a, -bCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice SSC JE tests.
Explore Courses for SSC JE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Download the FREE EduRev App
Track your progress, build streaks, highlight & save important lessons and more!