If 2x2+9+2x2−9=9+37 and 2x3+9−2x2−9=a−b, then

2x2+9+2x2−9=9+372x3+9−2x2−9=a−bComparisona=9,b=−37a=81,b=9×7=63

If 2x2+9+2x2−9=9+37 and 2x3+9−2x2−9=a−b, then

2x2+9+2x2−9=9+372x3+9−2x2−9=a−bComparisona=9,b=−37a=81,b=9×7=63

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If $\sqrt{2 x^{2} + 9} + \sqrt{2 x^{2} - 9} = 9 + 3 \sqrt{7}$ and $\sqrt{2 x^{3} + 9} - \sqrt{2 x^{2} - 9} = \sqrt{a} - \sqrt{b}$ , then

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$a = 9, b = 7$

$a = 63, b = 7$

$a = 81, b = 63$

$a = 63, b = 81$

answer is A.

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Detailed Solution

$\sqrt{2 x^{2} + 9} + \sqrt{2 x^{2} - 9} = 9 + 3 \sqrt{7}$

$\sqrt{2 x^{3} + 9} - \sqrt{2 x^{2} - 9} = \sqrt{a} - \sqrt{b}$

Comparison

$\sqrt{a} = 9, \sqrt{b} = - 3 \sqrt{7}$

$a = 81, b = 9 \times 7 = 63$

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