Question

Find the value of a and b in the following:
3+V7 = a +bV7
3-V7


[​V=is root]

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} }$

$\frac{ {3}^{2} + \sqrt{7} {}^{2} + 2 \times 3 \times \sqrt{7} }{ {3}^{2} - \sqrt{7} {}^{2} }$

$\frac{9 + 7 + 6 \sqrt{7} }{9 - 7}$

$\frac{16 + 6 \sqrt{7} }{2}$

$\frac{16}{2} + \frac{6 \sqrt{7} }{2}$

$8 + 3 \sqrt{7} = a + b \sqrt{7}$

So , a = 8 and b = 3