Question

Find value of a and b


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Answer 1

$\frac{ \sqrt{7 } - 3}{ \sqrt{7} + 3} = a \sqrt{7} + b \\ \\ \frac{7 - 6 \sqrt{7} + 9 }{4} \\ \\ \frac{16 - 16 \sqrt{7} }{4} \\ \\ - 4 \sqrt{7} + 4 \\ \\ a \: = - 4 \\ \\ b \: = 4$

Answer 2

Solution:-

Given:-

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

To Find :-

Value of a and b = ?

Find:-

$\frac{ \sqrt{7} - 3 }{ \sqrt{7} + 3 }$

Multiplying on Numerator and Denominator by ( √7 - 3).

$\frac{ \sqrt{7} - 3 }{ \sqrt{7} + 3 } \times \frac{ \sqrt{7} - 3 }{ \sqrt{7} - 3} \\ \\ \frac{ {( \sqrt{7} - 3) }^{2} }{( \sqrt{7} + 3)( \sqrt{7} - 3)} \\ \\ \frac{ { \sqrt{7} }^{2} + {3}^{2} - 2 \times \sqrt{7} \times 3 }{ { \sqrt{7} }^{2} - {3}^{2} } \\ \\ \frac{7 + 9 - 6 \sqrt{7} }{7 - 9} \\ \\ \frac{16 - 6 \sqrt{7} }{ - 2} \\ \\ - 8 + 3 \sqrt{7}$

According to the Given Information.

( √7 - 3)/(√7 + 3) = a√7 + b

=) 3√7 - 8 = a√7 + b

Hence,

a = 3.

And b = -8.