Question

5 + 3 root 2 by 5 minus 3 root 2 is equal to a + b root 2 find the value of a and b

Answer 1

Answer:

Here's your answer Plz mark BRAINLIEST ✌

Answer 2

Answer:

$\frac{43}{7} and \frac{30}{7}$  are the required value of a and b.

Step-by-step explanation:

Explanation:

Given in the question that, $\frac{5 + 3\sqrt{2} }{5 - 3\sqrt{2} }$ = $a + b\sqrt{2}$

So, we first rationalize $\frac{5 + 3\sqrt{2} }{5 - 3\sqrt{2} }$.

Rationalization - A rational number can be stated as the ratio of two integers, and rationalization is the process of changing an irrational number into one.

Step 1:

We have, LHS = $\frac{5 + 3\sqrt{2} }{5 - 3\sqrt{2} }$

⇒ $\frac{5 + 3\sqrt{2} }{5 - 3\sqrt{2} }$ × $\frac{5 + 3\sqrt{2} }{5 + 3\sqrt{2} }$

⇒ $\frac{(5 + 3\sqrt{2})^2 }{(5 - 3\sqrt{2})(5 + 3\sqrt{2} ) }$

⇒ $\frac{(25 + 30\sqrt{2} + 18) }{(25 - 18)}$ = $\frac{(43 + 30\sqrt{2} ) }{(7)}$

And this can be written as, $\frac{43}{7} + \frac{30\sqrt{2} }{7}$

Now, given in the question that,$\frac{5 + 3\sqrt{2} }{5 - 3\sqrt{2} }$ = $a + b\sqrt{2}$

So, on comparing $\frac{43}{7} + \frac{30\sqrt{2} }{7}$ and $a + b\sqrt{2}$ we get.

a = $\frac{43}{7}$ and b = $\frac{30 }{7}$

Final answer:

Hence,value of  a = $\frac{43}{7}$ and b = $\frac{30 }{7}$.

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