If a and b are rational numbers and 5+2root3 upon 7+4root3 = a-b root

1.	If a and b are rational numbers and 5+2root3 upon 7+4root3 = a-b root 3, find the value of a and b.
Answer» stion :- If a and B are RATIONAL numbers and $\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - b \sqrt{3}$ , FIND the values of a and b. Required SOLUTION :- $\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = \frac{5 + 2\sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = \frac{35 - 20 \sqrt{3 } + 14 \sqrt{3} - 8 \times 3}{ {7}^{2} - (4 \sqrt{3}) ^{2} }$ $\frac{11 - 6 \sqrt{3} }{49 - 48} = \frac{11 - 6 \sqrt{3} }{1} = 11 - 6 \sqrt{3}$ ∴ a - b $\sqrt{3}$ = 11 - 6 $\sqrt{3}$ ⟹ A = 11 and B = 6 $\text{[math]}$

If a and b are rational numbers and 5+2root3 upon 7+4root3 = a-b root 3, find the value of a and b.

Answer»

stion :-

If a and B are RATIONAL numbers and $\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - b \sqrt{3}$ , FIND the values of a and b.

Required SOLUTION :-

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = \frac{5 + 2\sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = \frac{35 - 20 \sqrt{3 } + 14 \sqrt{3} - 8 \times 3}{ {7}^{2} - (4 \sqrt{3}) ^{2} }$