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(C) Given equation: $x - \frac{1}{x} = \frac{45}{14}$Multiply by $x$ to clear the denominator: $\frac{x^2 - 1}{x} = \frac{45}{14}$Cross-multiply: $14(

Vedclass · Accepted Answer

$\frac{7}{2}$ and $-\frac{2}{7}$

Vedclass · Answer

(C) Given equation: $x - \frac{1}{x} = \frac{45}{14}$Multiply by $x$ to clear the denominator: $\frac{x^2 - 1}{x} = \frac{45}{14}$Cross-multiply: $14(x^2 - 1) = 45x$Rearrange into standard quadratic form $ax^2 + bx + c = 0$: $14x^2 - 45x - 14 = 0$Factorize by splitting the middle term: $14x^2 - 49x + 4x - 14 = 0$Group the terms: $7x(2x - 7) + 2(2x - 7) = 0$Factor out the common binomial: $(2x - 7)(7x + 2) = 0$Set each factor to zero: $2x - 7 = 0$ or $7x + 2 = 0$Solve for $x$: $x = \frac{7}{2}$ or $x = -\frac{2}{7}$Thus,the roots of the quadratic equation are $\frac{7}{2}$ and $-\frac{2}{7}$.

Solve the following equation using the method of factorization: $x - \frac{1}{x} = \frac{45}{14} \quad (x \neq 0)$

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