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Which is the number, which when squared and added to 12 becomes seven times its value ?

Sagot :

luana
[tex]x^{2}+12=7*x[/tex], where x is unknown numer

Now we are moving [tex]7*x[/tex] on left side to obtain quadratic equation:

[tex]x^{2}+12-7*x=0[/tex]

Our goal is to find two roots of this equation.

First we are finding delta:

[tex]\Delta =b^{2}-4*a*c[/tex]

[tex]\Delta =(-7)^{2}-4*1*12=1[/tex]

First root:

[tex]x_{1}=\frac{-b+\sqrt{\Delta}}{2*a}[/tex]

[tex]x_{1}=\frac{7+\sqrt{1 }}{2}=4[/tex]

Second root:

[tex]x_{2}=\frac{-b-\sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2}=\frac{7-\sqrt{1 }}{2}=3[/tex]
konrad509
[tex]x^2+12=7x\\ x^2-7x+12=0\\ x^2-3x-4x+12=0\\ x(x-3)-4(x-3)=0\\ (x-4)(x-3)=0\\ x=4 \vee x=3[/tex]
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