Question

4 + 3 root 5 upon 4 - 3 root 5 equals to a + b root 5

Answer 1

Answer:

$a=-\frac{61}{29}$ and $a=-\frac{24}{29}$

Step-by-step explanation:

Given : $\frac{4+3\sqrt{5}}{4-3\sqrt{5}}=a+b\sqrt{5}$

To find : The value of a and b?

Solution :

Taking LHS,

$\frac{4+3\sqrt{5}}{4-3\sqrt{5}}$

Rationalize the expression,

$=\frac{4+3\sqrt{5}}{4-3\sqrt{5}}\times\frac{4+3\sqrt{5}}{4+3\sqrt{5}}$

$=\frac{(4+3\sqrt{5})^2}{(4)^2-(3\sqrt{5})^2}$

$=\frac{16+45+24\sqrt5}{16-45}$

$=\frac{61+24\sqrt5}{-29}$

$=\frac{61}{-29}+\frac{24\sqrt5}{-29}$

On comparing with RHS,

$a=-\frac{61}{29}$ and $a=-\frac{24}{29}$

Answer 2

Answer:

a = -61/29 , b = -24/29

Step-by-step explanation:

for explanation please see the above photos. hope so it is helpful to you!