Solve x^2/ 98*3/ 97=x^4/96*5/95

Question

Solve the equation

x_{1} = - \frac{12 1843}{679}, x_{2} = 0, x_{3} = \frac{12 1843}{679}

Alternative Form

x_{1} \approx - 0.758707, x_{2} = 0, x_{3} \approx 0.758707

Evaluate

\frac{x ^{2}}{98} \times \frac{3}{97} = \frac{x ^{4}}{96} \times \frac{5}{95}

Multiply the terms

More Steps

\frac{3 x ^{2}}{9506} = \frac{x ^{4}}{96} \times \frac{5}{95}

Simplify

More Steps

\frac{3 x ^{2}}{9506} = \frac{x ^{4}}{1824}

Cross multiply

3 x^{2} \times 1824 = 9506 x^{4}

Simplify the equation

5472 x^{2} = 9506 x^{4}

Rewrite the expression

2 \times 2736 x^{2} = 2 \times 4753 x^{4}

Evaluate

2736 x^{2} = 4753 x^{4}

Add or subtract both sides

2736 x^{2} - 4753 x^{4} = 0

Factor the expression

x^{2} (2736 - 4753 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2736 - 4753 x^{2} = 0

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

x = 0 2736 - 4753 x^{2} = 0

Solve the equation

More Steps

x = 0 x = \frac{12 1843}{679} x = - \frac{12 1843}{679}

Solution

x_{1} = - \frac{12 1843}{679}, x_{2} = 0, x_{3} = \frac{12 1843}{679}

Alternative Form

x_{1} \approx - 0.758707, x_{2} = 0, x_{3} \approx 0.758707

Show Solution