Question

if 3+ √2 ÷3 - √2= a + b √2 find the value of a and b

Answer 1

Answer:

value ofa=11÷7;b=6÷7

Answer 2

Answer:

a = $\dfrac{11}{7}$ and b = $\dfrac{6}{7}$

Step-by-step explanation:

We have been given the equation:-

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

Rationalize the denominator:-

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

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

$\dfrac{9+2+6\sqrt{2}}{9-2} = a + b \sqrt{2}$

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

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

So, the value of a is $\dfrac{11}{7}$ and the value of b is $\dfrac{6}{7}$ !