Question

SOLVE THIS QUADRATIC EQUATION....

( BY SPLITTING THE MID-TERM METHOD)

THANKS FOR HELPING​

Answer 1

Step-by-step explanation:

$\frac{1}{x} - \frac{1}{x - 2} = 3$

By cross multiplication method, we get

$\frac{x - 2 - x}{x(x - 2)} = 3$

$\frac{ - 2}{ {x}^{2} - 2x} = 3$

$3( {x}^{2} - 2x) = - 2$

$3 {x}^{2} - 6x = - 2$

$3 {x}^{2} - 6x + 2 = 0$

Note:The roots of this quadratic equation cannot be found by splitting of middle term method.

So we have to use the formula to find the roots that is :

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

Here a =3,b =-6 and c=2.

Then,

$x = \frac{ - ( - 6) + - \sqrt{ {6}^{2} - 4 \times 3 \times 2 } }{2 \times 3}$

$x = \frac{ 6 + - \sqrt{36 - 24} }{6}$

$x = \frac{6 + \sqrt{12} }{6} \: or \: \frac{6 - \sqrt{12} }{6}$

Answer 2

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$\frac{1}{x}$-$\frac{1}{x-2}$=3

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$\red{\boxed{\blue{\underline{\orange{\mathrm{Proof:-}}}}}}$

*Cross multiply to get the Equation*

→$\frac{x-2-x}{(x)×(x-2)}$=3

→$\frac{-2}{x^2-2x}$=3

*Cross Multiply again*

→3×(x²-2x)=-2

→3x²-6x=2

→3x²-6x-2=0

S=-6[Sum of Equation]

P=-6[Product of Equation]

*As there is no Common factor, we can conclude that the Equation can be factorized by splitting the middle term method*

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So now we will use Discriminant formula↓

→Discriminant Formula:-

d=b²-4ac

a=3

b=-6

c=-2

→d=(-6)²-4×3×(-2)

→d=36+24

→d=60

→√d=±√60

→√d=±2√15

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taking x(+)=$\frac{-b+ \sqrt{d}}{2a}$

→$\frac{-(-6)+2 \sqrt{15}}{2×3}$

→$\frac{6+2 \sqrt{15}}{6}$

*Take 2 common*

→$\frac{\cancel{2}(3+ \sqrt{15}}{\cancel{6}}$

→$\frac{3+ \sqrt{15}}{3}$

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taking x(-)=$\frac{-b- \sqrt{d}}{2a}$

→$\frac{-(-6)-2 \sqrt{15}}{2×3}$

→$\frac{6-2 \sqrt{15}}{6}$

*Take 2 common*

→$\frac{\cancel{2}(3- \sqrt{15}}{\cancel{6}}$

→$\frac{3- \sqrt{15}}{3}$

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