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Definition of Function

If 6x-6x-3=...

Question

If $6^{x} - 6^{x - 3} = 7740$ , then $x^{x} =$

A

7796

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B

243

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C

3125

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D

46656

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Solution

The correct option is C 3125
$6^{x} - 6^{x - 3} = 7740$
$\Rightarrow 6^{x} - \frac{6^{x}}{6^{3}} = 7740$
$\Rightarrow 6^{x} (1 - \frac{1}{216}) = 7740$
$\Rightarrow 6^{x} \times \frac{215}{216} = 7740$
$\Rightarrow 6^{x} = \frac{7740 \times 216}{215} 36 \times 216 = 6^{5}$
$\Rightarrow x = 5$
$∴ x^{x} = 5^{5} = 3125$

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x = 2^{\frac{1}{3}} + 2^{\frac{2}{3}}

then the value of

x^{2} - 6 x + 6 x

x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}, t h e n x^{3} - 6 x^{2} + 6 x =

x = 2 + 2^{\frac{1}{3}} + 2^{\frac{2}{3}}

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

?

Q. The factors of x³ − 7x + 6 are

(a) x (x − 6) (x − 1)

(b) (x² − 6) (x − 1)

(c) (x + 1) (x + 2) (x + 3)

(d) (x − 1) (x + 3) (x − 2)

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then prove that

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