Which can be the value of k, if

Step-by-Step Solution
Simplify the Numerator:
Using the order of operations (BODMAS/PEMDAS), handle division and multiplication first:

(88 ÷ 8) * k = 11 * k = 11k

3 * 3 = 9

Numerator = 11k - 9

Simplify the Denominator:

6² = 36

7 * 5 = 35

Denominator = 36 - 35 + k² = 1 + k²

Set up the equation:
(11k - 9) / (1 + k²) = 1

Solve the quadratic equation:

Multiply both sides by (1 + k²):
11k - 9 = 1 + k²

Rearrange the terms into a standard quadratic form (ax² + bx + c = 0):
k² - 11k + 10 = 0

Factor the quadratic equation:
We need two numbers that multiply to 10 and add up to -11. Those numbers are -1 and -10.

(k - 1)(k - 10) = 0

Therefore, the possible values for k are 1 and 10.