Answer:
Number of boys in the park is 36
Step-by-step explanation:
Number of boys playing = x
Number of girls playing in park = ![\sqrt{x}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D)
Total children playing in the park = 42
Now, accoding to the question,
Number of Boys + Number of girls = Total children in park
![x + \sqrt{x} = 42](https://tex.z-dn.net/?f=x%20%2B%20%5Csqrt%7Bx%7D%20%20%20%3D%2042)
or, ![\sqrt{x} = 42 - x](https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%20%20%3D%2042%20-%20x)
Squaring both sides we get
![x = 1764 + x^{2} - 84x](https://tex.z-dn.net/?f=x%20%3D%20%201764%20%2B%20%20x%5E%7B2%7D%20%20%20-%2084x)
or, ![x^{2} - 85x + 1764 = 0](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%20-%2085x%20%20%20%20%2B%201764%20%20%3D%200)
or,
⇒(x-49)(x-36) = 0
⇒ either x = 49, or x = 36
if number of boys playing in the park is 49,
then number of girls = 42 -49 NOT POSSIBLE
⇒ x ≠ 49
Hence, x = 36 = Number of boys
And, Number of girls = 42 - 36 = 6