Question

find the value of a and b 5 + root 3 upon 7 minus 4 root 3 is equal a + b root 3​

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

7+4

3

5+2

3

=a+b

3

Since rationalization of

c+

d

a+

b

=

c+

d

a+

b

×

c−

d

c−

d

Taking L.H.S.

By rationalization,

7+4

3

5+2

3

=

7+4

3

5+2

3

×

7−4

3

7−4

3

Since, {(a+b)(a−b)=a

2

−b

2

}

=

[(7)

2

−(4

3

)

2

]

(5+2

3

)×(7−4

3

)

=

49−16

3

3

35+14

3

−20

3

−8

3

3

=

49−48

35−

3

(14−8)−24

=

1

35−

3

(6)−24

=11−6

3

Hence, by comparing a = 11 & b = -6.

Answer 2

Answer:

a = 47      and        b = 12

Step-by-step explanation:

here, $\frac{5 + \sqrt{3}}{7 - 4\sqrt{3}} = a + b\sqrt{3}$

     = $\frac{5 + \sqrt{3}}{7 - 4\sqrt{3}} * \frac{{7 + 4\sqrt{3}}}{{7 + 4\sqrt{3}}}$ $= a + b\sqrt{3}$

     = $\frac{35 + 5\sqrt{3} + 7\sqrt{3} +12}{7^{2} - 4\sqrt{3} ^{2} }$ $= a + b\sqrt{3}$

     = $\frac{47 + 12\sqrt{3}}{49 - 48}$ $= a + b\sqrt{3}$

     = $\frac{47 + 12\sqrt{3}}{1}$ $= a + b\sqrt{3}$

     = $47 + 12\sqrt{3}$ $= a + b\sqrt{3}$

so, a = 47      and        b = 12

hope it will help you.