Question

1. Questions 1 to 6 carry 2 marks each.
2. Questions 7 to 21 carry 3 marks each
3. Questions 22 to 30 carry 5 marks each.
4. All questions are compulsory.
5. There are no negative marks.
(ANSWER TO ALL QUESTIONS IN INTEGERS FROM 00 TO 99)
The lengths of the sides of a right triangle are the integers a, b and c, and these integers have no
common factor. If a <b< c and (c-a): b = 4:5, then find the value of (b + c-a).
The equation x - x2 = mx + 1 = 0 has two equal roots, distinct from the third root. Find the value of 5m.
3x - 2x + x +1 3x°- 2x + 5x-13
If the real number a, b, c satisfy the equation
, then find the value of
3x - 2x?-X-1 3x - 2x2 -5x +13
18(a + b + c).
Find the positive integer whose cube exceeds its square by 4624.
The number of ordered pairs of real numbers (a, b) for which 3 x - 2y + =10 and x = a + b.
VX-20
Find the number of ordered pairs of integers (x, y) such that (2x + y) (5x + 3y) = 7
_125
1,0 < x < 90. If the rar
If [x] denotes the greatest integer not greater than x and​

Answer 1

Answer:

X = 17

Step-by-step explanation:

Find the positive integer whose cube exceeds its square by 4624.

Let say number = X

Than cube = X³

X³ = X² + 4624

=> X³ - X² - 4624 = 0

=> X³ - 17X² + 16X² - 272X + 272X - 4624 = 0

=> X²(X - 17) + 16X(X - 17) + 272(X - 17) = 0

=> (X - 17) (X² + 16X + 272) = 0

=>  X = 17  

for X² + 16X + 272  D < 0 so no real solution