Question

Nationalised the denominator and find the values of a and b 3+√7/3-√7=a+b√7​

Answer 1

Answer:

a=16, b=6.

Step-by-step explanation:

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7} \\ \frac{3 + \sqrt{7} }{3 - \sqrt{7} } \: \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } =a + b \sqrt{7} \\ \frac{(3 + \sqrt{7})( 3 + \sqrt{7} )}{3 - 7} = a + b \sqrt{7} \: \\ \frac{9 + 6 \sqrt{7} + 7 }{4} =a + b \sqrt{7} \\ \frac{16 + 6 \sqrt{7} }{4} = a + b \sqrt{7} \: \\ 16 + 6 \sqrt{7} = 4(a + b \sqrt{7}) \\ 16 + 6 \sqrt{7} = 4a + 4b \sqrt{7}$

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