Solve (n-2)*x^2 (n-3)*x^6-n=0

Evaluate

(n - 2) x^{2} (n - 3) x^{6} - n = 0

Multiply the terms

More Steps

x^{8} (n - 2) (n - 3) - n = 0

Rewrite the expression

(n^{2} - 5 n + 6) x^{8} - n = 0

Move the expression to the right-hand side and change its sign

(n^{2} - 5 n + 6) x^{8} = 0 + n

Add the terms

(n^{2} - 5 n + 6) x^{8} = n

Divide both sides

\frac{( n ^{2} - 5 n + 6 ) x ^{8}}{n ^{2} - 5 n + 6} = \frac{n}{n ^{2} - 5 n + 6}

Divide the numbers

x^{8} = \frac{n}{n ^{2} - 5 n + 6}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 8 \frac{n}{n ^{2} - 5 n + 6}

Simplify the expression

More Steps

x = \pm \frac{8 ( n ^{2} - 5 n + 6 ) ^{7} n}{∣ n ^{2} - 5 n + 6 ∣}

Solution

x = \frac{8 ( n ^{2} - 5 n + 6 ) ^{7} n}{∣ n ^{2} - 5 n + 6 ∣} x = - \frac{8 ( n ^{2} - 5 n + 6 ) ^{7} n}{∣ n ^{2} - 5 n + 6 ∣}

Solve the equation