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Popular >

(x^{12}-1)8=x^{84}-1

Solution

(x^{12} - 1) 8 = x^{84} - 1

Solution

+1

Decimal Notation

x = 1, x = - 1, x = 1.00361 \dots, x = - 1.00361 \dots

Solution steps

(x^{12} - 1) \cdot 8 = x^{84} - 1

Expand

(x^{12} - 1) \cdot 8 : 8 x^{12} - 8

8 x^{12} - 8 = x^{84} - 1

Switch sides

x^{84} - 1 = 8 x^{12} - 8

Move

8

to the left side

x^{84} + 7 = 8 x^{12}

Move

8 x^{12}

to the left side

x^{84} + 7 - 8 x^{12} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{84} - 8 x^{12} + 7 = 0

Rewrite the equation with

u = x^{2}, u^{6} = x^{12}

and

u^{42} = x^{84}

u^{42} - 8 u^{6} + 7 = 0

Solve

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 1 : x = 1, x = - 1

Solve

x^{2} = - 1 :

No Solution for

x \in R

Solve

Solve

No Solution for

x \in R

The solutions are

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