What are the roots of a equation (a+b+x)1 = a...
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
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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.
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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?
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