AP EAMCET · Maths · Quadratic Equation
If \((3+\sqrt{2})^6-(3-\sqrt{2})^6=a+b \sqrt{2}\), then \(a+b=\)
- A \(5220\)
- B \(5230\)
- C \(5240\)
- D \(5250\)
Answer & Solution
Correct Answer
(A) \(5220\)
Step-by-step Solution
Detailed explanation
\(\because(3+\sqrt{2})^6-(3-\sqrt{2})^6=a+b \sqrt{2}\) ...(i) \(\begin{aligned} & \text { Let } x=3+\sqrt{2} \text { and } y=3-\sqrt{2} \\ & x^2+y^2=9+2+6 \sqrt{2}+9+2-6 \sqrt{2}=22 \\ & x^3+y^3=(3+\sqrt{2})^3+(3-\sqrt{2})^3\end{aligned}\)…
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