Question

2+5√7/2-5√7 = a+√7b Plz step by step solution

Answer 1

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Answer 2

$\mathbf{ \frac{2 + 5 \sqrt{7} }{2 - 5 \sqrt{7} } = a + b \sqrt{7} }$

$\mathbf{ By \: \: Rationalization } \\ \\ \frac{2+5\sqrt{7} }{ 2 - 5\sqrt{7} } \times \frac{2 + 5\sqrt{7} }{ 2 + 5\sqrt{7} } \\ \\ \frac{ ( 2 + 5\sqrt{7}) ( 2 + 5\sqrt{7})}{ ( 2 - 5\sqrt{7}) (2 + 5\sqrt{7})} \\ \\ \frac{4 + 175+ 20\sqrt{7}}{4 - 175 } \\ \\ \frac{ - 179 - 20\sqrt{7}}{171}$

On comparing values, we get

a = -179 / 171

b = - 20 / 171