Answer:
a = 97, b = - 56
Step-by-step explanation:
Given
[tex]\frac{7-4\sqrt{3} }{7+4\sqrt{3} }[/tex]
To rationalise multiply numerator/ denominator by the conjugate of the denominator.
The conjugate of 7 + 4[tex]\sqrt{3}[/tex] is 7 - 4[tex]\sqrt{3}[/tex]
= [tex]\frac{(7-4\sqrt{3})(7-4\sqrt{3}) }{(7+4\sqrt{3})(7-4\sqrt{3}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{49-28\sqrt{3}-28\sqrt{3}-48 }{49-48}[/tex]
= [tex]\frac{97-56\sqrt{3} }{1}[/tex]
= 97 - 56[tex]\sqrt{3}[/tex]
with a = 97 and b = - 56
