Question

If root2+root 7/ root2-root 7= a+b root a,b

Answer 1

Answer:

${a}^{2}b + a {b}^{2} = \frac{137 + 36 \sqrt{14} }{25}$

Step-by-step explanation:

$\frac{ \sqrt{2} + \sqrt{7} }{ \sqrt{2} - \sqrt{7} } = (a + b) \sqrt{ab} \\ = \frac{ \sqrt{2} + \sqrt{7} }{ \sqrt{2} - \sqrt{7} } \times \frac{ \sqrt{2} + \sqrt{7} }{ \sqrt{2} + \sqrt{7} } = (a + b) \sqrt{ab} \\ = \frac{2 + 2\sqrt{14} + 7 }{2 - 7} = (a + b) \sqrt{ab} \\ = ({ \frac{9 + 2 \sqrt{14} }{ - 5} })^{2} = (a + b) {ab} \\ = \frac{81 + 56 + 36 \sqrt{14} }{25} = (a + b)ab \\ = \frac{137 + 36 \sqrt{14} }{25} = (a + b)ab \\ = {a}^{2}b + a {b}^{2} = \frac{137 + 36 \sqrt{14} }{25}$

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