Question

If (30k)2 = 3600, then which of the following cannot
be triangular number?​

Answer 1

Answer:

2k + 1  cannot be triangular number.

Step-by-step explanation:

Consider the provided equation.

$(30k)^2 = 3600$

Solve the above equation as shown:

$30k= \sqrt{3600}$

$30k= \pm 60$

$k=\pm 2$

The value of K is ±2

This is the Triangular Number Sequence are:

1, 3, 6, 10, 15, 21, 28, 36, 45, ...

We need to identify which cannot be a triangular number

For this we will put the value of k in the provided options and check whether the value of the equation is a triangular number or not.

Let say we have some options:

(1) 4+k

(2) 5-k

(3) 2k + 1

(4) 2k-3

Substitute K=2 in 4+k

4+2=6 which is a triangular number, so 4+k  can be triangular number.

Substitute K=2 in 5-k

5-2=3 which is a triangular number, so 5-k   can be triangular number.

Substitute K=2 in 2k + 1

2(2) + 1=5  which is not a triangular number,

Now, substitute k=-2 in 2k + 1

2(-2) + 1 = -3 This is also not a triangular number, so this 2k + 1  cannot be triangular number.

Substitute K=2 in 2k-3

2(2)-3=1 which is a triangular number, so 2k-3   can be triangular number.

Similarly, you can check whether your option is correct or not by substituting the value of k.