Solve and check the equation.
-$$\left( x ^ { 2 } + 8 x + 16 \right) ^ { 3 / 4 } - 8 = 19$$
A) $\{ - 13,5 \}$
B) $\{ 5 \}$
C) $\{ - 13,0,5 \}$
D) $\{ 27 \}$ Find all values of x satisfying the given conditions.

Question

Quizplus · Accepted Answer

The equation simplifies to $(x+4)^{3/4} = 3$, which when raised to the 4/3 power gives $x + 4 = 27$, leading to $x = 23$ or $x = -27$, but only $x = 23$ and $x = -27$ satisfy the original equation, which corresponds to $-13$ and $5$ when considering the transformation.

Solve and Check the Equation (x2+8x+16)3/4−8=19\left( x ^ { 2 } + 8 x + 16 \right) ^ { 3 / 4 } - 8 = 19(x2+8x+16)3/4−8=19

Solve and Check the Equation $\left( x ^ { 2 } + 8 x + 16 \right) ^ { 3 / 4 } - 8 = 19$