Question

If x belongs to N find the number of solution of x square + X - 400 is lesser or equal to zero

Answer 1

Step-by-step explanation:

'x' value is greater than zero

Answer 2

19 Possible solution for x² + x - 400 ≤ 0 if x ∈ N

Given:

• x² + x - 400 is lesser or equal to zero
• x ∈ N

To Find:

• Number of solutions

Solution:

(a + b)² = a² + 2ab + b²

x² + x - 400 ≤ 0

Step 1 :

Add 400 both sides

x² + x ≤  400

Step 2 :

Add (1/2)² = 1/4  both sides

x² + x + (1/2)² ≤  400  + 1/4

x² + 2(x)(1/2)  ≤  400  + 1/4

Step 3 :

Use identity (a + b)² = a² + 2ab + b²

(x + 1/2)² ≤  400  + 1/4

(x + 1/2)² ≤  1601/4

Step 4 :

Taking square root both sides

| x + 1/2) ≤  ≈20.006

x + 1/2 < 20.006    when x + 1/2  ≥ 0

x <  19.506

x from 1 to 19     as x ∈ N

x + 1/2  ≥ - 20       x + 1/2 < 0   not possible as x ∈ N

Hence 19 possible solution