Let x = (sqrt{50} + 7)^{1/3} - (sqrt{50} - 7) | vedclass

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(A) Given,$x = (\sqrt{50} + 7)^{1/3} - (\sqrt{50} - 7)^{1/3}$.Cubing both sides,we use the identity $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$:$x^3 = (\sqrt

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$x = 2$

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(A) Given,$x = (\sqrt{50} + 7)^{1/3} - (\sqrt{50} - 7)^{1/3}$.Cubing both sides,we use the identity $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$:$x^3 = (\sqrt{50} + 7) - (\sqrt{50} - 7) - 3[(\sqrt{50} + 7)(\sqrt{50} - 7)]^{1/3} \cdot x$Simplify the terms:$x^3 = 14 - 3(50 - 49)^{1/3} \cdot x$$x^3 = 14 - 3(1)^{1/3} \cdot x$$x^3 = 14 - 3x$Rearrange the equation:$x^3 + 3x - 14 = 0$By testing values,we find that $x = 2$ is a root because $2^3 + 3(2) - 14 = 8 + 6 - 14 = 0$.Factoring the polynomial:$(x - 2)(x^2 + 2x + 7) = 0$The quadratic factor $x^2 + 2x + 7$ has a discriminant $D = 2^2 - 4(1)(7) = 4 - 28 = -24 Thus,the only real solution is $x = 2$.

Let $x = (\sqrt{50} + 7)^{1/3} - (\sqrt{50} - 7)^{1/3}$. Then,

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