Solve the equation after making an appropriate substitution.
-$$x ^ { 4 } - 50 x ^ { 2 } + 49 = 0$$
A) $\{ - 49,49 \}$
B) $\{ - 50,50 \}$
C) $\{ - 1,1 , - 7,7 \}$
D) $\{ - 7,7 \}$

Question

Quizplus · Accepted Answer

This equation resembles a quadratic equation if we substitute $x^2 = y$, turning it into $y^2 - 50y + 49 = 0$. Solving this quadratic equation yields $y = 1$ and $y = 49$. Reverting the substitution ($x^2 = y$) gives us $x^2 = 1$ and $x^2 = 49$, leading to the solutions $x = \pm 1$ and $x = \pm 7$, hence the correct answer is $\{ - 1,1 , - 7,7 \}$.

Solve the Equation After Making an Appropriate Substitution x4−50x2+49=0x ^ { 4 } - 50 x ^ { 2 } + 49 = 0x4−50x2+49=0

Solve the Equation After Making an Appropriate Substitution $x ^ { 4 } - 50 x ^ { 2 } + 49 = 0$