Question

Let$x=(\sqrt{50}+7{)}^{\frac{1}{3}}-(\sqrt{50}-7{)}^{\frac{1}{3}}$

• A. x = 2
• B. x = 3
• C. x is a rational number, but not an integer
• D. x is irrational number

Answer 1

The correct option is A

x = 2

$(\sqrt{5}0+7{)}^{\frac{1}{3}}=tx=t-\frac{1}{t}{x}^3=t^3-\frac{1}{t^3}-3(t-\frac{1}{t})x^3+3x=\sqrt{50}+7-(\sqrt{50}-7)x^3+3x=14x^3+3x-14=0(x-2\left)\right(x^2+2x+7)\Rightarrow x=2$