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Yanka [14]
3 years ago
9

Solve x^2+ 17x-12=-84

Mathematics
1 answer:
kramer3 years ago
4 0

Answer:

(X+9)(X+8)=0

X=-9,-8

Step-by-step explanation:

x^2+ 17x-12=-84

x^2+17x-12+84=0

x^2+17x+72=0

x^2+(9+8)X+72=0

x^2+9x+8x+72=0

X(X+9)+8(X+9)=0

(X+9)(X+8)=0

X=-9,-8

So the value of the X is -9,-8

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This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex
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L(x,y,z,\lambda)=8x+8y+4z+\lambda(4x^2+4y^2+4z^2-36)

L_x=8+8\lambda x=0\implies 1+\lambda x=0
L_y=8+8\lambda y=0\implies 1+\lambda y=0
L_z=4+8\lambda z=0\implies 1+2\lambda z=0
L_\lambda=4x^2+4y^2+4z^2-36=0\implies x^2+y^2+z^2=9

yL_x=y+\lambda xy=0
xL_y=x+\lambda xy=0
\implies yL_x-xL_y=y-x=0\implies y=x

2zL_x=2z+2\lambda xz=0
xL_z=x+2\lambda xz=0
\implies 2zL_x-xL_z=2z-x=0\implies x=2z

2zL_y=2z+2\lambda yz=0
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\implies 2zL_y-yL_z=2z-y=0\implies y=2z

x=y=2z\implies x^2+y^2+z^2=9\iff 4z^2+4z^2+z^2=9z^2=9\implies z=\pm1

z=\pm1\implies y=x=\pm2

So we have two critical points, (2, 2, 1) and (-2, -2, -1), which respectively give a max of 36 and a min of -36.
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