In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘x’ and ‘y’ and mark correct answer.
I. x4 – 18x2 + 81 = 0
II. y4 – 25y2 + 144 = 0
Solution
Correct Answer: Option E
We will solve both the equations separately.
Equation I:
x4 – 18x2 + 81 = 0
let x2 = a, then
a2 – 18a + 81 = 0
⇒ a2 – 2 × a × 9 + (9)2 = 0
By using the formula: (a + b)2 = a2 + 2ab + b2
(a – 9)2 = 0
a = 9, 9
So, x = ±3, ±3
Equation II.
y4 – 25y2 + 144 = 0
let y2 = b
⇒ b2 – 25b + 144 = 0
⇒ b2 – 16b – 9b + 144 = 0
⇒ b(b – 16) – 9(b – 16) = 0
⇒ (b – 9) (b – 16) = 0
⇒ b = 9, 16
So, y = ±3, ±4
Comparing the values of x and y, we get,
Few value of x are greater than y and few are smaller, same is true for y too. So, relation cannot be determined.
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