Question

In the following question, two equations are given. Solve both the equations and mark the corresponding answer, if:

a) x is greater than y

b) x is less than y

c) x is greater than or equal than y

d) x is less than or equal to y

e) x = y or a definite relationship between x & y cannot be established

I.x${}^2$ - 19x + 84 = 0

II. y${}^2$ - 25y + 156 = 0

• A. (a)
• B. (b)
• C. (d)
• D. (e)

Answer 1

The correct option is C

(d)

x${}^2$ - 19 x + 84 = 0

=$>$ x${}^2$ - 12 x - 7 x + 84 = 0

=$>$ x(x - 12) - 7 (x - 12) = 0

=$>$ (x - 7) (x - 12) = 0

So, x = 7 or x = 12

y${}^2$ - 25 y + 156 = 0

=$>$ y${}^2$ - 12 y - 13 y + 156 = 0

=$>$ y(y - 12) - 13 (y - 12) = 0

=$>$ (y - 13) (y - 12) = 0

So, y = 12 or 13

Thus, we see that x$\le$ y