Solve: $y ^ { 4 } - 10 y ^ { 2 } + 9 = 0$
A) $\{ 9,1 \}$
B) $\{ 3,1 \}$
C) $\{ 3 , - 3,1 , - 1 \}$
D) $\{ - 9 , - 1 \}$

Question

Quizplus · Accepted Answer

Let's make a substitution: $x=y^2$
Then we get:
$$x^2-10x+9=0$$
$$(x-9)(x-1)=0$$
So $x = 9$ or $x = 1$.
Substituting back $y^2$ for $x$, we get:
$$y^4-10y^2+9=(y^2-9)(y^2-1)=(y-3)(y+3)(y-1)(y+1)=0$$
Therefore, the solutions for the equation are $y=3, y=-3, y=1, y=-1$, which corresponds to choice C.

Solve y4−10y2+9=0y ^ { 4 } - 10 y ^ { 2 } + 9 = 0y4−10y2+9=0

Solve $y ^ { 4 } - 10 y ^ { 2 } + 9 = 0$