Answer:
11-6√3 = a -b√3
where a=11 and b =6
Step-by-step explanation:
Step(i):-
Given
[tex]\frac{5+2\sqrt{3} }{7+4\sqrt{3} }[/tex]
Rationalize
= [tex]\frac{5+2\sqrt{3} }{7+4\sqrt{3} } X \frac{7-4\sqrt{3} }{7-4\sqrt{3} }[/tex]
= [tex]\frac{(5+2\sqrt{3})(7-4\sqrt{3} ) }{7^{2} -(4\sqrt{3})^{2} }[/tex]
= [tex]\frac{(5+2\sqrt{3})(7-4\sqrt{3} ) }{49-16(3) }[/tex]
= [tex]\frac{(5+2\sqrt{3})(7-4\sqrt{3} ) }{1 }[/tex]
Step(ii):-
Multiply
[tex]{(5+2\sqrt{3})(7-4\sqrt{3} ) }[/tex]
= 5 × 7 - 5×4√3 + 2√3 ×7 - 2√3 × 4√3
= 35 -20√3+ 14√3-8×3
= 35 - 6√3 -24
= 11-6√3
