Question

Solve the equation using formula:
√6х² – 4х – 2√6 = 0​

Answer 1

Answer:x= root6,-2/ root6

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Answer 2

Given:-

p(x)=√6x²-4x-2√6

To Find:-

The value of x?

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

We can start by using the Discriminant formula.

♦Formula↓

d=b²-4ac

Using the Formula↑

a=√6

b=-4

c=-2√6

→d=(-4)²-4×√6×-2√6

→d=16+48

→d=64

→√d=±√64

→√d=±8

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

→x=$\frac{-(-4)+8}{2× \sqrt{6}}$

→x=$\frac{\cancel{12}}{\cancel{2}\sqrt{6}}$

♦x=$\frac{6}{\sqrt{6}}$

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★Rationalizing the Denominator★

→Multiply by √6

→$\frac{6× \sqrt{6}}{\sqrt{6}× \sqrt{6}}$

→$\frac{\cancel{6} \sqrt{6}}{\cancel{6}}$

→√6

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

→x=$\frac{-(-4)-8}{2× \sqrt{6}}$

→x=$\frac{\cancel{-4}}{\cancel{2}\sqrt{6}}$

♦x=$\frac{-2}{\sqrt{6}}$

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★Rationalizing the Denominator★

→Multiply by √6

→$\frac{-2× \sqrt{6}}{\sqrt{6}× \sqrt{6}}$

→$\frac{\cancel{-2} \sqrt{6}}{\cancel{6}}$

→$\frac{ \sqrt{6}}{3}$

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