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Sagot :

Answer:

The  given equation is of the form

p( x+ q)² + r   =  [tex]3((x+(-\frac{7}{6})^{2} +(-\frac{61}{12})[/tex]

Step-by-step explanation:

Step(i):-

Given equation  3 x² - 7 x -1

                =  [tex]3(x^{2} -\frac{7}{3} x )-1[/tex]

                = [tex]3(x^{2} -2 X \frac{7}{3X2} +(\frac{7}{6} )^{2}-(\frac{7}{6} ^{2} )-1[/tex]

               = [tex]3(x^{2} -2 X \frac{7}{6} +(\frac{7}{6} )^{2}-(\frac{49}{36} )) -1[/tex]

Step(ii):-

We know that formula

(a-b)² = a² - 2ab + b²

[tex]3x^{2} -7x-1 = 3((x-\frac{7}{6})^{2} -( 3X\frac{49}{36} )) -1[/tex]

[tex]3x^{2} -7x-1 = 3((x-\frac{7}{6})^{2} -\frac{61}{12}[/tex]

Final answer:-

The  given equation is of the form

p( x+ q)² + r   =  [tex]3((x+(-\frac{7}{6})^{2} +(-\frac{61}{12})[/tex]

                     

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