Question

Find a and b if 3-2 root 2/3+2 root 2=a+b root 2

Answer 1

Answer:

$\frac{3 - 2\sqrt{2} }{3 + 2 \sqrt{2} } = a + b \sqrt{2}$

Or,

$\frac{(3 - 2 \sqrt{2} )(3 - 2 \sqrt{2}) }{(3 + 2 \sqrt{2})(3 - 2 \sqrt{2})} = a + b \sqrt{2}$

Or,

$\frac{ {(3 - 2 \sqrt{2}) }^{2}}{ {(3)}^{2} - ( {2 \sqrt{2})}^{2} } = a + b \sqrt{2}$

Or,

$\frac{9 + 8 - 12 \sqrt{2} }{9 - 8} = a + b \sqrt{2}$

Or,

$\frac{17 - 12 \sqrt{2} }{1} = a + b \sqrt{2}$

Or,

$17 - 12 \sqrt{2} = a + b \sqrt{2}$

Comparing both side, we get

$a = 17$

$b = - 12$

Step-by-step explanation:

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