WBJEE · Maths · Quadratic Equation
The equation \(6^{x}+8^{x}=10^{x}\) has
- A no real root
- B infinitely many rational roots
- C exactly one real root
- D two distinct real roots
Answer & Solution
Correct Answer
(C) exactly one real root
Step-by-step Solution
Detailed explanation
\(6^{x}+8^{x}=10^{x}\left(\frac{3}{5}\right)^{x}+\left(\frac{4}{5}\right)^{x}=1 \Rightarrow\left(\frac{3}{5}\right)^{x}=1-\left(\frac{4}{5}\right)^{x}\) \(\therefore \quad 6^{x}+8^{x}=10^{x}\) has exactly one real root
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