Question

4+3/3=A+VB, then B - A is Ex.3. If 77 +473 (1) -13 (3) 13 (2) 2213 (4) 373 - 77

11th - 12th Class

Maths

Solution

108

4.0 (1 ratings)

Sol. (3) ( sqrt{7+4 sqrt{3}}=sqrt{7+2 times 2 times sqrt{3}} ) ( =sqrt{4+3+2 times 2 times sqrt{3}}=sqrt{(2+sqrt{3})^{2}}=2+sqrt{3} ) ( therefore frac{4+3 sqrt{3}}{2+sqrt{3}}=A+sqrt{B} ) ( Rightarrow frac{(4+3 sqrt{3})(2-sqrt{3})}{(2+sqrt{3})(2-sqrt{3})}=A+sqrt{B} ) ( Rightarrow frac{8-4 sqrt{3}+6 sqrt{3}-9}{4-3}=A+sqrt{B} ) ( Rightarrow 2 sqrt{3}-1=A+sqrt{B} Rightarrow A=-1 ) and ( sqrt{B}=2 sqrt{3} ) ( Rightarrow mathrm{B}=2 sqrt{3} times 2 sqrt{3}=12 ) ( therefore B-A=12+1=13 )