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In the following question two equations are given. You have to solve these equations and determine relation between a and b. I. a2 - a - 156 = 0 II. b2 - b - 210 = 0

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

I. a2 - a - 156 = 0

II. b2 - b - 210 = 0
1). a < b
2). a > b
3). a = b or the relationship cannot be determined
4). a ≥ b


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1 answers

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Answered by on | Votes 1 |

I. a2 - a - 156 = 0

⇒ a2 - 13a + 12a - 156 = 0

⇒ a(a - 13) + 12(a - 13) = 0

⇒ (a - 13)(a + 12) = 0

Then, a = 13 or a = -12

II. b2 - b - 210 = 0

⇒ b2 –15b + 14 + 210 = 0

⇒ b(b - 15) + 14(b - 15) = 0

⇒ (b - 15)(b + 14) = 0

Then, b = 15 or b = -14

So, when a = 13, a < b for b = 15 and a > b for b = -14

And when a = -12, a < b for b = 15 and a > b for b = -14

∴ We can observe that a = b or the relationship cannot be determined.

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