Question:
If for a particular value of the variable \(x\), the following holds true: \(17 = \dfrac{17x}{1-x}\), then find the value of \(x^{2x}\).
If for a particular value of the variable \(x\), the following holds true: \(17 = \dfrac{17x}{1-x}\), then find the value of \(x^{2x}\).
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Simplify the equation first, the 17s cancel, solve for x, then substitute into the exponent expression.
Updated On: Jul 15, 2026
- 17
- 1
- 2
- 1/2
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The Correct Option is D
Solution and Explanation
Step 1: Set up the equation.
We are given 17 = 17x/(1-x). Since 17 appears as a common factor on both sides, once directly and once inside the fraction's numerator, we can simplify before cross-multiplying.
Step 2: Divide both sides by 17.
Dividing both sides by 17 gives: 1 = x/(1-x). This removes the common factor and leaves a simpler equation in x.
Step 3: Cross-multiply to remove the fraction.
Multiplying both sides by (1 - x): 1 - x = x.
Step 4: Solve for x.
1 - x = x gives 1 = 2x, so x = 1/2.
Step 5: Substitute x into the required expression.
We need the value of x^(2x). With x = 1/2, the exponent 2x = 2 x 1/2 = 1. So the expression becomes x^(2x) = (1/2)^1 = 1/2.
Step 6: Match with the options.
The value 1/2 corresponds to option (4). This confirms the answer.
We are given 17 = 17x/(1-x). Since 17 appears as a common factor on both sides, once directly and once inside the fraction's numerator, we can simplify before cross-multiplying.
Step 2: Divide both sides by 17.
Dividing both sides by 17 gives: 1 = x/(1-x). This removes the common factor and leaves a simpler equation in x.
Step 3: Cross-multiply to remove the fraction.
Multiplying both sides by (1 - x): 1 - x = x.
Step 4: Solve for x.
1 - x = x gives 1 = 2x, so x = 1/2.
Step 5: Substitute x into the required expression.
We need the value of x^(2x). With x = 1/2, the exponent 2x = 2 x 1/2 = 1. So the expression becomes x^(2x) = (1/2)^1 = 1/2.
Step 6: Match with the options.
The value 1/2 corresponds to option (4). This confirms the answer.
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