Solve 467x^23=23x^467 - Socratic AI (ScanMath)

问题

Solve the equation

x_{1} = - \frac{2158941}{1541}, x_{2} = 0, x_{3} = \frac{2158941}{1541}

Alternative Form

x_{1} \approx - 0.953494, x_{2} = 0, x_{3} \approx 0.953494

Evaluate

467 x^{2} \times 3 = 23 x^{4} \times 67

Multiply the terms

1401 x^{2} = 23 x^{4} \times 67

Multiply the terms

1401 x^{2} = 1541 x^{4}

Add or subtract both sides

1401 x^{2} - 1541 x^{4} = 0

Factor the expression

x^{2} (1401 - 1541 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1401 - 1541 x^{2} = 0

The only way a power can be 0 is when the base equals 0

x = 0 1401 - 1541 x^{2} = 0

Solve the equation

更多步骤

Evaluate

1401 - 1541 x^{2} = 0

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

- 1541 x^{2} = 0 - 1401

Removing 0 doesn't change the value,so remove it from the expression

- 1541 x^{2} = - 1401

Change the signs on both sides of the equation

1541 x^{2} = 1401

Divide both sides

\frac{1541 x ^{2}}{1541} = \frac{1401}{1541}

Divide the numbers

x^{2} = \frac{1401}{1541}

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

x = \pm \frac{1401}{1541}

Simplify the expression

更多步骤

Evaluate

\frac{1401}{1541}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1401}{1541}

Multiply by the Conjugate

\frac{1401 \times 1541}{1541 \times 1541}

Multiply the numbers

\frac{2158941}{1541 \times 1541}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2158941}{1541}

x = \pm \frac{2158941}{1541}

Separate the equation into 2 possible cases

x = \frac{2158941}{1541} x = - \frac{2158941}{1541}

x = 0 x = \frac{2158941}{1541} x = - \frac{2158941}{1541}

解题方案

x_{1} = - \frac{2158941}{1541}, x_{2} = 0, x_{3} = \frac{2158941}{1541}

Alternative Form

x_{1} \approx - 0.953494, x_{2} = 0, x_{3} \approx 0.953494

显示解题方案