If (5+2 √(3))/(7+4 √(3))=a+b √(3), then · ABC26GN1442
Subject: General Aptitude · Chapter: Square Roots and Cube Roots · Exam: R.R.B. 2010
If $\frac{5+2 \sqrt{3}}{7+4 \sqrt{3}}=a+b \sqrt{3}$, then
(a)$a=-11, b=-6$
(b)$a=-11, b=6$
(c)$a=11, b=-6$
(d)$a=6, b=11$
Answer
Explanation
$a+b \sqrt{3}=\frac{(5+2 \sqrt{3})}{(7+4 \sqrt{3})} \times \frac{(7-4 \sqrt{3})}{(7-4 \sqrt{3})}=\frac{35-20 \sqrt{3}+14 \sqrt{3}-24}{(7)^{2}-(4 \sqrt{3})^{2}}$
Explanation as extracted from the printed page; notation may be imperfect.
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