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Solve \(\sqrt{14+17 x-2 x^{2}}=x+2\)
in Mathematics by Platinum (109k points) | 215 views

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Best answer
To remove the square root sign square both sides:

\[14+17x-2x^2=x^2+4x+4\]

move all terms to the left hand side:

\[2x^2+x^2+4x-17x-14+4=0\]

 

group like terms

\[3x^2-13x-10=0\]

i.e.

\[3x^2-3x-10x-10=0\]

\[3x(x-1)-10(x-1)=0\]

\[(x-1)(3x-10)=0\]

\[\therefore x=1 \quad OR \quad x=\dfrac{10}{3}\]
by Platinum (109k points)

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