Question

if on = mn, find mn.
a. 4
b. 5
c. $4\sqrt{2}$
d. $4\sqrt{30}$

Explanation:

$$x^3+7x^2-32x-224=0$$
$$x^2(x+7)-32(x+7)=0$$
$$(x^2-32)(x+7)=0$$
$$x^2=32 \to x=4\sqrt2$$
So answer is C. $4\sqrt2$, but option B is 5. I must have misread the diagram: maybe LO=8, OM=7, then:
$$2x^2=7^2=49 \to x^2=24.5 \text{ no.}$$
Wait, the problem says "If ON=MN, find

Answer:

$$x^3+7x^2-32x-224=0$$
$$x^2(x+7)-32(x+7)=0$$
$$(x^2-32)(x+7)=0$$
$$x^2=32 \to x=4\sqrt2$$
So answer is C. $4\sqrt2$, but option B is 5. I must have misread the diagram: maybe LO=8, OM=7, then:
$$2x^2=7^2=49 \to x^2=24.5 \text{ no.}$$
Wait, the problem says "If ON=MN, find