Solve the quadratic equation 36x^2−12ax+(a^2−b^2 )=0 – InterviewSolution

1.

Solve the quadratic equation 36x^2−12ax+(a^2−b^2 )=0

Answer»

Step-by-step explanation:

The given quadratic equation is:

${36x}^{2} \: - 12ax \: + ( {a}^{2} \: - \: {b}^{2} ) \: = 0$

THEREFORE, COMPARING with general form,

${ax}^{2} \: - bx \: + c \: = 0$

we GET,

$a = 36 \\ b = - 12a \\ c = ( {a}^{2} \: - \: {b}^{2} )$

By using formula,

$x \: = \: - b \: \frac{ + }{ - } \frac{\sqrt{ {b}^{2} \: - \: 4ac } }{2a}$

Now,

$x \: = \: - ( - 12a) \: \frac{ + }{ - } \frac{\sqrt{ { - 12a}^{2} \: - \: 4(36)( {a}^{2} - {b}^{2} )} }{2(36)}$

$x \: = \: -12a \: \: \frac{ + }{ - } \frac{\sqrt{ {144a}^{2} \: - 144( {a}^{2} \: - \: {b}^{2} )} }{2(36)}$

$x \: = \: -12a \: \: \frac{ + }{ - } \frac{\sqrt{ {144a}^{2} \: - 144 {a}^{2} \: + \: 144{b}^{2} } }{72}$

$x \: = \: -12a \: \: \frac{ + }{ - } \frac{\sqrt{ \: 144{b}^{2} } }{72}$

$x \: = \: -12a \: \: \frac{ + }{ - } \frac{12b }{72}$

$x \: = \frac{a \: + \: b}{6}$

Or

$x \: = \frac{a \: - \: b}{6}$

I HOPE it help for.

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