Subject
Quantitative Aptitude
Topic
Algebra
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
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
ক)
x > yখ)
x ≥ yগ)
x < yঘ)
x ≤ yঙ)
x = y or the relation cannot be determinedExplanation
We will solve both the equations separately. Equation I: x 4 – 18x 2 + 81 = 0 let x 2 = a, then a 2 – 18a + 81 = 0 ⇒ a 2 – 2 × a × 9 + (9) 2 = 0 By using the formula: (a + b) 2 = a 2 + 2ab + b 2 (a – 9)2 = 0 a = 9, 9 So, x = ±3, ±3 Equation II. y 4 – 25y2 + 144 = 0 let y 2 = b ⇒ b 2 – 25b + 144 = 0 ⇒ b 2 – 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.Related questions
if then what would be the value of ?Multiplication and difference of two numbers are 93 and 28 respectively. Find the difference of reciprocals of the numbers.if , then find the value of In following question, two equations are given, you have to solve them and choose the correct option:
x2– 3x – 4 = 0,
y2– 4 = 0In following question, two equations are given, you have to solve them and chose the correct option:
x2+ 11x + 30 = 0,
y2+ 7y + 12 = 0In the following question, one or two equation(s) is/are given. You have to solve both the equations and find the relation between ‘l’ and ‘m’ and mark correct answer.
I. (125)1/3l – (1331)1/3= 4 × (729)1/6+ (1024)1/10II. (m)2– (15625)1/3= 0Direction: In the following question two equations numbered I and II are given. You have to solve both the equations and give answers:I: x - √121 = 0
II: y2- 121 = 0The number of solutions of x2+ 4|x| + 5 = 0 is