Question

Find a and b if 3-2√2/3+2√2=a+b√2

Answer 1

Answer:

a=17 and b=-12

Step-by-step explanation:

$\frac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } = a + b \sqrt{2} \\ \frac{3 - 2 \sqrt{2} }{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } = a + b \sqrt{2} \\ \frac{(3) ^{2} + (2 \sqrt{2}) ^{2} - 2(3)(2 \sqrt{2} ) }{(3) ^{2} - (2 \sqrt{2} ) ^{2} } = a + b \sqrt{2} \\ \frac{9 + 8 - 12 \sqrt{2} }{9 - 8} = a + b \sqrt{2} \\ 17 - 12 \sqrt{2} = a + b \sqrt{2}$

Comparing the both sides, we get

a=17 and b = -12