Question

Find the value of a and b if

5-root3 upon root 5 + root 3 = (1/2) a + 3b root 15 ?

guys its urgent plz dont post any irrelevant answers I would really appreciate those who give the correct answer and mark as branliest​

Answer 1

Answer:

do let me know if its incorrect

Answer 2

Answer:

The value of a = 8 and the value of b =   $\frac{-1}{3}$

Step-by-step explanation:

Given,

$\frac{\sqrt{5} - \sqrt{3} }{\sqrt{5} + \sqrt{3} } = \frac{1}{2}a + 3b\sqrt{15}$

To find,

The value of 'a' and 'b'

Solution,

L H S = $\frac{\sqrt{5} - \sqrt{3} }{\sqrt{5} + \sqrt{3} }$

The rationalizing factor = $\sqrt{5} - \sqrt{3}$

Multiply the numerator and denominator with the rationalizing factor, we get

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

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

= $\frac{5 + 3 - 2\sqrt{15} }{2}$

= $\frac{8 - 2\sqrt{15} }{2}$

= 4 - $\sqrt{15}$

Since  $\frac{\sqrt{5} - \sqrt{3} }{\sqrt{5} + \sqrt{3} } = \frac{1}{2}a + 3b\sqrt{15}$, we have

4 - $\sqrt{15}$ $= \frac{1}{2}a + 3b\sqrt{15}$

Comparing the rational and irrationals on both sides we get,

4 = $\frac{1}{2}a$

a = 8

$3b\sqrt{15}$ = $-\sqrt{15}$

3b = -1

b = $\frac{-1}{3}$

The value of a = 8 and the value of b =  $\frac{-1}{3}$

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