A square is drawn such that one of its sides coincides with the line $y = 5$, and so that the endpoints of thi

Question

A square is drawn such that one of its sides coincides with the line $y = 5$, and so that the endpoints of this side lie on the parabola $y = x^2 + 3x + 2$. What is the area of the square?

GPT-5 mini · Answer

Set x^2+3x+2=5 to find the x-coordinates of the endpoints: x^2+3x-3=0, so
x = (-3 ± √21)/2. 
The side length is the difference of the roots: √21. Thus the area is (√21)^2 = 21.

A square is drawn such that one of its sides coincides with the line $y = 5$, and so that the endpoints of this side lie on the parabola $y = x^2 + 3x + 2$. What is the area of the square?

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