Answer:
x = - 10, x = 10
Step-by-step explanation:
Given
- 7 + [tex](x^2-19)^{\frac{3}{4} }[/tex] = 20 ( add 7 to both sides )
[tex](x^2-19)^{\frac{3}{4} }[/tex] = 27 , that is
[tex]\sqrt[4]{(x^2-19)^{3} }[/tex] = 27 ( raise both sides to the power of 4 )
(x² - 19)³ = [tex]27^{4}[/tex] = 531441 ( take the cube root of both sides )
x² - 19 = [tex]\sqrt[3]{531441}[/tex] = 81 ( add 19 to both sides )
x² = 100 ( take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
solution is x = - 10, x = 10
