x^2+15x+sqrt(x^2+15x)=20

해법

x^{2} + 15 x + x^{2} + 15 x = 20

x = 1, x = - 16

솔루션 단계

x^{2} + 15 x + x^{2} + 15 x = 20

제곱근 제거

x^{2} + 15 x = x^{4} + 30 x^{3} + 185 x^{2} - 600 x + 400

x^{2} + 15 x = x^{4} + 30 x^{3} + 185 x^{2} - 600 x + 400

해결 :

x = 1, x = - 16, x = \frac{- 15 + 5 13}{2}, x = \frac{- 15 - 5 13}{2}

x = 1, x = - 16, x = \frac{- 15 + 5 13}{2}, x = \frac{- 15 - 5 13}{2}

솔루션 확인:

x = 1

참

, x = - 16

참

, x = \frac{- 15 + 5 13}{2}

거짓

, x = \frac{- 15 - 5 13}{2}

거짓

해결책은

x = 1, x = - 16