Question

What is the value of (a+b) in the expressions 4 / 3- root 5 = a+b root 5 ?

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Answer 1

Answer:

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

First rationalize the value in L.H.S

that is

$\frac{4}{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \frac{4(3 + \sqrt{5} )}{ {3}^{2} - \sqrt{5} ^{2} } \\ = \frac{12 + 4 \sqrt{5} }{9 - 5} = \frac{12 + 4 \sqrt{5} }{4}$

therefore

$a + b \sqrt{5} = \frac{12 + 4 \sqrt{5} }{4} \\ = \frac{12}{4} + \frac{4 \sqrt{5} }{4}$

Comparing L.H.S & R.H.S

we get

$a = \frac{12}{4} = 3\\ b \sqrt{5} = \frac{4 \sqrt{5} }{4} = \frac{2(2 \sqrt{5} )}{4} = \frac{2 \sqrt{5} }{2} \\ b \sqrt{5} = \frac{2 \sqrt{5} }{2}$

If B√5= (2√5)/2

Then B= 1

Then B= 1and A=3

hope it helps

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