Question

What are the solutions of the equation x^4-9x^2+8=0? Use u substitution to solve

Answer 1

Exact Form:
x
=
2
√
2
,
−
2
√
2
,
−
1
,
1
x
=
2
2
,
-
2
2
,
-
1
,
1
Decimal Form:
x
=
2.82842712
…
,
−
2.82842712
…
,
−
1
,
1

Answer 2

Answer with Step-by-step explanation:

We have to solve the equation:

$x^4-9x^2+8=0$

let u=x²

u²-9u+8=0

⇒ u²-8u-u+8=0

⇒ u(u-8)-1(u-8)=0

⇒ (u-8)(u-1)=0

⇒ u=8 or u=1

⇒ x²=8 or x²=1

⇒ x=2√2 or x=-2√2 or x=1 or x=-1

Hence, Solution of $x^4-9x^2+8=0$ is:

x=2√2 ,-2√2,1 and-1