AP EAMCET · Maths · Quadratic Equation
If \((3+2 \sqrt{2})^{x^2-4}+(3-2 \sqrt{2})^{x^2-4}=6\), then \(x^4+x^2+5=\)
- A -30
- B -35
- C 30
- D 35
Answer & Solution
Correct Answer
(D) 35
Step-by-step Solution
Detailed explanation
Since \((3+2 \sqrt{2}) \cdot(3-2 \sqrt{2})=9-8=1\) \[ \Rightarrow(3-2 \sqrt{2})=\frac{1}{(3+2 \sqrt{2})} \] Now \((3+2 \sqrt{2})^{x^2-4}+(3-2 \sqrt{2})^{x^2-4}=6\) \[ \Rightarrow(3+2 \sqrt{2})^{x^2-4}+\frac{1}{(3+2 \sqrt{2})^{x^2-4}}=6 \] Let \(y=(3+2 \sqrt{2})^{x^2-4}\)…
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