Question

The value of $x$ and $y$ in the following equation :
$\sqrt{(5330{)}_x+(1425{)}_y}=(50{)}_x+(15{)}_y$

• A. $(x,y)=(7,6)$
• B. $(x,y)=(6,7)$
• C. $(x,y)=(7,8)$
• D. $(x,y)=(8,7)$

Answer 1

The correct option is B $(x,y)=(6,7)$

$\begin{array}{cc}(5330{)}_x& =5\times x^3+3\times x^2+3\times x\\ & =5x^3+3x^2+3x\\ (1425{)}_y& =1\times y^3+4\times y^2+2\times y+5\\ & =y^3+4y^2+2y+5\\ (50{)}_x& =5\times x=5x\\ (15{)}_y& =1\times y+5=5+y\\ \text{Putting values from given options,}& \\ x& =6\\ \text{and}y& =7\text{satisfies given relation}\\ \therefore (x,y)& =(6,7)\end{array}$