$\frac{3}{x ^{2}} + \frac{4}{x} = 5$

Answer

$x_{1} = 1.10349 x_{4} = - 0.25465 - 0.92208 i x_{2} = - 0.59419 x_{3} = - 0.25465 + 0.92208 i$

Explanation

\frac{3}{x ^{2}} + \frac{4}{x} x^{2} x \cdot \frac{3}{x ^{2}} + x^{2} x \cdot \frac{4}{x} \frac{3}{x ^{1}} + 4 x^{1} \cdot \frac{3}{x ^{1}} + x^{1} \cdot 4 3 + 4 x 3 + 4 x - 5 x^{4} - 5 x^{4} + 4 x + 3 = 5 = x^{2} x \cdot 5 = 5 x^{3} = x^{1} \cdot 5 x^{3} = 5 x^{4} = 0 = 0 multiply ALL terms by x^{2} x . cancel out the denominators multiply ALL terms by x^{1} . cancel out the denominators move all terms to the left hand side simplify left side

This polynomial has no rational roots that can be found using Rational Root Test.

Roots were found using quartic formulas

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x23​+x4​=5

x1​=1.10349x4​=−0.25465−0.92208i​x2​=−0.59419​x3​=−0.25465+0.92208i

$\frac{3}{x ^{2}} + \frac{4}{x} = 5$

$x_{1} = 1.10349 x_{4} = - 0.25465 - 0.92208 i x_{2} = - 0.59419 x_{3} = - 0.25465 + 0.92208 i$