f-x-x-4-g-x-36-x-2-3-Find-points-of-intersection-

Question Number 56878 by ajfour last updated on 25/Mar/19

f (x) = ∣∣ x ∣ - 4 ∣

g (x) = \sqrt{36 - x^{2}} - 3

Find points of intersection .

Answered by mr W last updated on 25/Mar/19

l e t t =∣ x ∣, 0 ⩽ t ⩽ 6

i f t ⩽ 4 :

\sqrt{36 - t^{2}} - 3 = 4 - t

\sqrt{36 - t^{2}} = 7 - t

36 - t^{2} = 49 - 14 t + t^{2}

2 t^{2} - 14 t + 13 = 0

t = \frac{7 - \sqrt{23}}{2} < 4 \Rightarrow o k

\Rightarrow x = \pm \frac{7 - \sqrt{23}}{2}

i f 4 ⩽ t ⩽ 6 :

\sqrt{36 - t^{2}} - 3 = t - 4

\sqrt{36 - t^{2}} = t - 1

36 - t^{2} = t^{2} - 2 t + 1

2 t^{2} - 2 t - 35 = 0

t = \frac{1 + \sqrt{71}}{2} > 4 \Rightarrow o k

\Rightarrow x = \pm \frac{1 + \sqrt{71}}{2}

Commented by ajfour last updated on 26/Mar/19

Thank you Sir .

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