Question

$I.x^2-24x+144=0$
$II.y^2-26y+169=0$

• A. $x<y$
• B. $x>y$
• C. $x=y$
• D. $x\ge y$
• E. $x\le y$ or no relationship can be established between x and y

Answer 1

The correct option is A $x<y$

Equation I
$x^2-24x+144=0$
$\Rightarrow x^2-12x+12x+144=0$
$\Rightarrow x(x-12)-12(x-12)=0$
$\Rightarrow (x-12)(x-12)=0$
$\Rightarrow (x-12{)}^2=0$
$\therefore x=12$
Equation II
$y^2-26y+169=0$
$\Rightarrow y^2-13y-13y+169=0$
$\Rightarrow y(y-13)-13(y-13)=0$
$\Rightarrow (y-13{)}^2=0$
$\therefore y=13$
Hence, y > x
Alternate method
Equation I
$x^2-24x+144=0$
$x^2-2\left(12\right)\left(x\right)+(12{)}^2=0$
$\Rightarrow (x-12{)}^2=0$
$\therefore x=12$
Equation II
$y^2-26y+169=0$
$y^2-2\left(13\right)\left(y\right)+(13{)}^2=0$
$\Rightarrow (y-13{)}^2=0$
$\therefore y=13$
Hence, y > x