Question

Find the values of 'a' and 'b'
5+3 square root 2/5-3 square root 2=a+b square root 2

Answer 1

Answer:

a=43/7 b=40/7

Step-by-step explanation:

$\frac{(5 + 3 \sqrt{2} )}{(5 - 3 \sqrt{2}) } = a + b \sqrt{2} \\ \frac{(5 + 3 \sqrt{2} )(5 + 3 \sqrt{2}) }{(5 - 3 \sqrt{2} )(5 + 3 \sqrt{2}) } = a + b \sqrt{2} \\ \frac{25 + 18 + 30 \sqrt{2} }{25 - 18} = a + b \sqrt{2} \\ \frac{43 + 30 \sqrt{2} }{7} = a + b \sqrt{2} \\ \frac{43}{7} + \frac{30}{7} \times \sqrt{2} = a + b \sqrt{2} \\ then \: we \: have \: \\ a = \frac{43}{7} and \: b = \frac{30}{7}$