x+2=sqrt(r^2-x^2)

解

x + 2 = r^{2} - x^{2}

x = \frac{- 4 + 8 r ^{2} - 16}{4} {r \leq - 2 or r \geq 2}, x = \frac{- 4 - 8 r ^{2} - 16}{4} {- 2 \leq r \leq - 2 or 2 \leq r \leq 2}

解答ステップ

x + 2 = r^{2} - x^{2}

両辺を2乗する:

x^{2} + 4 x + 4 = r^{2} - x^{2}

x^{2} + 4 x + 4 = r^{2} - x^{2}

解く

x^{2} + 4 x + 4 = r^{2} - x^{2} : x = \frac{- 4 + 8 r ^{2} - 16}{4}, x = \frac{- 4 - 8 r ^{2} - 16}{4}

x = \frac{- 4 + 8 r ^{2} - 16}{4}, x = \frac{- 4 - 8 r ^{2} - 16}{4}

解を検算する:

x = \frac{- 4 + 8 r ^{2} - 16}{4} {r \leq - 2 or r \geq 2}, x = \frac{- 4 - 8 r ^{2} - 16}{4} {- 2 \leq r \leq - 2 or 2 \leq r \leq 2}

解答は

x = \frac{- 4 + 8 r ^{2} - 16}{4} {r \leq - 2 or r \geq 2}, x = \frac{- 4 - 8 r ^{2} - 16}{4} {- 2 \leq r \leq - 2 or 2 \leq r \leq 2}