Answer:

The two numbers are -9 and -5 or 6 and 10.

Step-by-step explanation:

Let

• s be the smaller number
• l be the larger number ([tex]l=s+4[/tex])

[tex]s^{2}+3l=66\\s^{2}+3(s+4)=66\\s^{2}+3s+12=66\\s^{2}+3s+12-66=0\\s^{2}+3s-54=0\\[/tex]

Factor out

[tex](s+9)(s-6)\\s=-9 and s=6[/tex]

Using [tex]s=-9[/tex]

[tex]l=s+4\\l=(-9)+4\\l=-5\\[/tex]

using [tex]s=6[/tex]

[tex]l=s+4\\l=(6)+4\\l=10\\[/tex]

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