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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?
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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.
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.
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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 2025 is part of SSC preparation. The Question and answers have been prepared according to the SSC 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 2025 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?.
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 2025 is part of SSC preparation. The Question and answers have been prepared according to the SSC 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 2025 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?.
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