Question

$I.8x^2-78x+169=0$
$II.20y^2-117y+169=0$

• A. x > y
• B. x $\ge$ y
• C. x < y
• D. x $\le$ y
• E. x = y or the relationship cannot be established

Answer 1

The correct option is A x > y

Equation I
$8x^2-78x+169=0$
$\Rightarrow 8x^2-52x-26x+169=0$
$\Rightarrow 4x(2x-13)-13(2x-13)=0$
$\Rightarrow (2x-13)(4x-13)=0$
$\therefore x=\frac{13}{2}or\frac{13}{4}=6.5or325$
Hence, x $\ge$ y
Equation II
$20y^2-117y+169=0$
$\Rightarrow 20y^2-52y-65y+169=0$
$\Rightarrow 4y(5y-3)-13(5y-13)=0$
$\Rightarrow (5y-13)(4y-13)=0$
$\therefore x=\frac{13}{5}or\frac{13}{4}=2.6or325$
Hence, x $\ge$ y