Question

find the value of a and b ,if 3+√2/3-✓2=a+b✓2

Answer 1

multiplication of 3+√2 in both numerator and deno.
(3+√2)²/3²-(√2)²
5+6√2/5
a=5/5=1
b=6/5

Answer 2

Answer:

⇒ a = 11/7 and b = 6/7

Step-by-step explanation:

We have ,

$= > \frac{3 + \sqrt{2} }{3 - \sqrt{2} }$

$= > \frac{3 + \sqrt{2} }{(3 - \sqrt{2}) } \times \frac{(3 + \sqrt{2}) }{(3 + \sqrt{2}) }$

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

$= > \frac{3^{2} + ( \sqrt{2})^{2} + 2 \times 3 \times \sqrt{2} }{9 - 2}$

$= > \frac{9 + 2 + 6 \sqrt{2} }{7}$

$= > \frac{11 + 6 \sqrt{2} }{7}$

∴ 3 + √2 / 3 - √2 = a + b√2

Comparing on both the sides , we get ;

$= > \frac{11}{7} + \frac{6}{7} \sqrt{2} = a + b \sqrt{2}$

$= > a = \frac{11}{7} \: and \: b = \frac{6}{7}$