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In the following question two equations are given. You have to solve these equations and determine relation between x and y. I. x2 – 18x – 115 = 0 II. y2 + 22y + 112 = 0

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In the following question two equations are given. You have to solve these equations and determine relation between x and y.

I. x2 – 18x – 115 = 0

II. y2 + 22y + 112 = 0
1). x < y
2). x > y
3). x = y OR the relationship cannot be determined
4). x ≥ y


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3 vote
Answered by on | Votes 3 |

I. x2 – 18x – 115 = 0

⇒ x2 – 23x + 5x – 115 = 0

⇒ x(x – 23) + 5(x – 23) = 0

⇒ (x – 23)(x + 5) = 0

Then, x = + 23 or x = - 5

II. y2 + 22y + 112 = 0

⇒ y2 + 14y + 8y + 112 = 0

⇒ y(y + 14) + 8(y + 14) = 0

⇒ (y + 14)(y + 8) = 0

Then, y = - 14 or y = - 8

So, when x = + 23, x > y for y = - 14 and x > y for y = - 8

And when x = - 5, x > y for y = - 14 and x > y for y = - 8

∴ So, we can clearly observe that x > y.

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