Question

find the value of a and b, If
(4+3√5)/(4-3√5) = a + b√5

Answer 1

Rationalising denominator
(4+3√5)/(4-3√5)*(4+3√5)(4+3√5)
(4+3√5)²/(4-3√5)(4+3√5)
(4²+2(4)(3√5)+3√5)²)/(4²-(3√5)²)
[16+24√5+9(5)]/16-9(5)
[16+24√5+45]/16-45
61+24√5/-29
-(64+24√5)/29
-64/29+(-24√5)/29
=a+b√5

a=-64/29
b=-24/29

hope this helps you

Answer 2

Step-by-step explanation:

$\frac{(4 + 3 \sqrt{5} )}{(4 - 3 \sqrt{5} )} = a + b \sqrt{5} \\ rationalising \: denominator...... \\ \frac{ {(4 + 3 \sqrt{5} )}^{2} }{16 - 45} = a + b \sqrt{5} \\ \frac{16 + 24 \sqrt{5} + 45}{ - 29} = a + b \sqrt{5} \\ \frac{61 + 24 \sqrt{5} }{ - 29} = a + b \sqrt{5} \\ a = - \frac{61}{29} \\ b = \frac{24}{29}$