Question

Exercises 177–179 will help you prepare for the material covered in the next section. If −8-8 is substituted for x in the equation 5x23+11x13+2=0 $$5x^{\frac{2}$${3}} + $$11x^{\frac{1}$${3}} + 2 = 0 , is the resulting statement true or false?

Accepted Answer

First, recognize that the equation given is $$5x^{\frac{2}$${3}} + $$11x^{\frac{1}$${3}} + 2 = 0$$. We need to substitute x = -8$ into this equation and check if the resulting statement is true or false. Next, calculate x$$^{\frac{1}$${3}}$$ when $$x = -8. $$Since the exponent $$\frac{1}{3}$$ represents the cube root, find $$\sqrt[3]{-8}. $$Then, use the value of $$x^{\frac{1}$${3}}$$ to find x$$^{\frac{2}$${3}}. $$Recall that $$x^{\frac{2}$${3}} = \$$left(x^{\frac{1}$${3}}\$$right)^2. $$Substitute the values of $$x^{\frac{2}$${3}}$$ and x$$^{\frac{1}$${3}}$$ back into the original equation: $$5x^{\frac{2}$${3}} + $$11x^{\frac{1}$${3}} + 2$$. Finally, simplify the expression step-by-step and determine if the result equals zero. If it does, the statement is true; if not, it is false.

Exercises 177–179 will help you prepare for the material covered in the next section. If $negative 8$ is substituted for x in the equation $5 x^{\frac{2}{3}} + 11 x^{\frac{1}{3}} + 2 = 0$ , is the resulting statement true or false?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Evaluating Expressions with Rational Exponents

Substitution in Algebraic Equations

Checking the Validity of an Equation

Exercises 177–179 will help you prepare for the material covered in the next section. If −8-8 is substituted for x in the equation 5x23+11x13+2=0 5x^{\(\frac{2}{3}\)} + 11x^{\(\frac{1}{3}\)} + 2 = 0 , is the resulting statement true or false?