Question

In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:
I. $x^2+20=9x$
II. $y^2+42=13y$

• A. if x y
• B. if x > y
• C. if x y
• D. if x < y
• E. if x = y, or no definite relationship can be established between x and y

Answer 1

The correct option is D if x < y

$I.x^2-9x+20=0x^2-5x-4x+20=0x(x-5)-4(x-5)=0(x-4)(x-5)=0\therefore x=4or5$

$II.y^2-13y+42=0\Rightarrow y^2-7y-6y+42=0\Rightarrow y(y-7)-6(y-7)=0\Rightarrow (y-6)(y-7)=0\therefore y=6or7$