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(A) Given the equation: $x - \frac{20}{x} = 1$Multiply the entire equation by $x$ to eliminate the fraction: $x^2 - 20 = x$Rearrange the equation into

Vedclass · Accepted Answer

$5, -4$

Vedclass · Answer

(A) Given the equation: $x - \frac{20}{x} = 1$Multiply the entire equation by $x$ to eliminate the fraction: $x^2 - 20 = x$Rearrange the equation into the standard quadratic form $ax^2 + bx + c = 0$: $x^2 - x - 20 = 0$To factorize,find two numbers that multiply to $-20$ and add to $-1$: These numbers are $-5$ and $4$.Rewrite the middle term: $x^2 - 5x + 4x - 20 = 0$Group the terms: $x(x - 5) + 4(x - 5) = 0$Factor out the common binomial: $(x - 5)(x + 4) = 0$Set each factor to zero: $x - 5 = 0$ or $x + 4 = 0$Thus,the solutions are $x = 5$ or $x = -4$.

Solve the following equation using the method of factorization: $x - \frac{20}{x} = 1$

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