AP EAMCET · Maths · Quadratic Equation
The coefficient of the highest power of \(x\) in the expansion of \(\left(x+\sqrt{x^2-1}\right)^8+\left(x-\sqrt{x^2-1}\right)^8\) is
- A \(64\)
- B \(128\)
- C \(256\)
- D \(512\)
Answer & Solution
Correct Answer
(C) \(256\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Since }\left(x+\sqrt{x^2-1}\right)^8+\left(x-\sqrt{x^2-1}\right)^8 \\ & =2\left\{\begin{array}{r} { }^8 C_0 x^8+{ }^8 C_2 x^6\left(x^2-1\right)+{ }^8 C_4 x^4\left(x^2-1\right)^2 \\ \left.+{ }^8 C_6 x^2\left(x^2-1\right)^3+{ }^8 C_8…
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