Question

if A and B are rational numbers and 4 + 3 root 5 by 4 minus 3 root 5 is equal to a + b root 5 find a& b

Answer 1

Hey friend, Harish here.

Here is your answer:

Given that,

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


Now rationalize by multiplying and dividing with the conjugate. 

The conjugate of denominator is 4 - 3√5.

Then,

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

→$\frac{(4+3 \sqrt{5})^{2} }{16 - 45 } = a+b \sqrt{5}$

→$\frac{16+45+2(4)(3 \sqrt{5}) }{-29} = a + b \sqrt{5}$

→$\frac{61+ 24 \sqrt{5} }{-29} = a+b \sqrt{5}$

→$\frac{61}{-29} + \frac{24 \sqrt{5} }{-29} = a+b \sqrt{5}$

Now , by comparing we get ,

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

$b = \frac{-24}{29}$
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Hope my answer is helpful to you. Mark as brainliest if u like.

Answer 2

Answer:

Step-by-step explanation: