Solve the equation by making an appropriate substitution.
-$$x ^ { 4 } - 29 x ^ { 2 } + 100 = 0$$
A) $\{ - 2,2 , - 5,5 \}$
B) $\{ 4,25 \}$
C) $\{ 2,5 \}$
D) $\{ - 2 i , 2 i , - 5 i , 5 i \}$

Question

Quizplus · Accepted Answer

This equation can be solved by substituting $y = x^2$, resulting in a quadratic equation $y^2 - 29y + 100 = 0$. Solving this gives $y = 25$ or $y = 4$. Substituting back $x^2 = y$, we get $x^2 = 25$ which gives $x = 5$ or $x = -5$, and $x^2 = 4$ which gives $x = 2$ or $x = -2$. Thus, the solution set is $\{-5, -2, 2, 5\}$.

Solve the Equation by Making an Appropriate Substitution x4−29x2+100=0x ^ { 4 } - 29 x ^ { 2 } + 100 = 0x4−29x2+100=0

Solve the Equation by Making an Appropriate Substitution $x ^ { 4 } - 29 x ^ { 2 } + 100 = 0$