Question

If 5+2 root 3 / 5 - 2 root 3 = a+b root 3 find a and

Answer 1

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Answer 2

The value of  $a=\frac{28}{13}$  and  $b=\frac{20}{13}$.

Step-by-step explanation:

Given : Expression $\frac{5+2\sqrt3}{5-2\sqrt3}=a+b\sqrt3$

To find : The value of a and b ?

Solution :

$\frac{5+2\sqrt3}{5-2\sqrt3}=a+b\sqrt3$

Rationalize the denominator,

$\frac{5+2\sqrt3}{5-2\sqrt3}\times \frac{5+2\sqrt3}{5+2\sqrt3}=a+b\sqrt3$

$\frac{(5+2\sqrt3)^2}{5^2-(2\sqrt3)^2}=a+b\sqrt3$

$\frac{25+3+20\sqrt3}{25-12}=a+b\sqrt3$

$\frac{28+20\sqrt3}{13}=a+b\sqrt3$

$\frac{28}{13}+\frac{20\sqrt3}{13}=a+b\sqrt3$

$\frac{28}{13}+\frac{20}{13}\sqrt3=a+b\sqrt3$

On comparing,

The value of $a=\frac{28}{13}$ and $b=\frac{20}{13}$.

#Learn more

Find a and b if 2 root 5 + root 3 / 2 root 5 minus root 3 + 2 root 5 minus root 3 / 2 root 5 + root 3 is equal to a + root 15 b​

https://brainly.in/question/9760084