Question

Find values of a and b each of √7-2/√7+2=a√7+b

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{7} - 2 }{ \sqrt{7} + 2} = a \sqrt{7} + b$

Let us rationalise the denominator.

$\frac{ \sqrt{7} - 2 }{ \sqrt{7} + 2} \times \frac{ \sqrt{7} - 2}{ \sqrt{7} - 2 } = a \sqrt{7} + b$

$\frac{ { (\sqrt{7} - 2) }^{2} }{( \sqrt{7} + 2)( \sqrt{7} - 2) } = a \sqrt{7} + b$

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

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

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

By comparing both terms,

b = 3

a = -4